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# Permutations Or Combinations Of A Set Of Numbers

## I want to output every combination of a set of numbers. These permutations must include combinations that use only a few of the numbers as well as all eight...ie. 1, 1,2 1,2,3 as well as 1,2,3,4,5,6,7,8 The macro below is from http://www.j-walk.com/ss/excel/tips/tip46.htm This only produces combinations using every number. I'm not sure how this macro works but hopefully someone with better know how could run with it or break it down for me! I only need to achieve this once but am pretty sure doing it manually will cause error and or madness Dim CurrentRowSub GetString() Dim InString As String InString = InputBox("Enter text to permute:") If Len(InString) < 2 Then Exit Sub If Len(InString) >= 8 Then MsgBox "Too many permutations!" Exit Sub Else ActiveSheet.Columns(1).Clear CurrentRow = 1 Call GetPermutation("", InString) End IfEnd SubSub GetPermutation(x As String, y As String)' The source of this algorithm is unknown Dim i As Integer, j As Integer j = Len(y) If j < 2 Then Cells(CurrentRow, 1) = x & y CurrentRow = CurrentRow + 1 Else For i = 1 To j Call GetPermutation(x + Mid(y, i, 1), _ Left(y, i - 1) + Right(y, j - i)) Next End IfEnd Sub

Related Forum Messages:
All Combinations/Permutations
I must first thank the forums for the amazing help in making my life just a little easier, especially member "shg" for helping set up the VBA code to help me.

So I have a sheet to develop all possible combinations of units, the letters with their associated values above, as well as the maximum number of units possible. The user inputs a top value, this is followed by some subtraction leading to a working value with a tolerance level in which the sum of the combinations needs to remain within.

What my predicament is that while the VBA code in the attached book works to develop most combinations, when I input a small number such as 405, the combinations that arise are not complete. The results are shown in the attached workbook: show combinations of H and PP, but any human can read that there should also be 2 HN in the results, as the math add's up to within the tolerance level.

Combinations (not Permutations)
You will find a VBA Code for a PRIVATE example - displaying all 6 numbers combinations out of 10 (1-10).

My code displays them (in column "A") BUT What my question to you is - does someone have a General/Universal code to handle other kinds of combinations.

To my opinion, the usage of Nested (For-Next) Loops will not be the ideal solution - so maybe by using VBA Recursion ?

Generating Permutations And Combinations
For Ex:- If there are three Items.. A B C and forming a group of 2
then the the total no of combinations would be permut(3,1) = 6...

I need this to be shown as follows depending on the no of itmes and no of group no=2 in this case...

Permuations & Combinations are as follows:

AB
AC
BC
CA
CB
BA

Combinations/Permutations Of Values
I have a number 23753.2570, to be precise.

in another column, i have 400 rows filled with different numbers, from 1.4 to 23000,7840.

I need to find out all the possible combinations of which numbers from that 400 can make up 23753.2570.

so if my number was 40,000, and i had 4 cells with 10,000 in them, the outcome will be:

"There are 4 possible combination to your value"
then paste it into a new worksheet with the results
[cell1] = 10000 + [cell2] = 10000 + [cell3] = 10000 + [cell4] = 10000
Total = 40000

i found this code, but i tested it on the example above and it said "All Combinations exhausted" which they wasn't?

Sub findsums()

'This *REQUIRES* VBAProject references to
'Microsoft Scripting Runtime
'Microsoft VBScript Regular Expressions 1.0 or higher

Const TOL As Double = 0.000001 'modify as needed
Dim c As Variant

All Combinations Or Permutations From 2 Lists
I've got what I think is a pretty interesting problem, not sure if it can be solved with Excel, and if not that's fine I'll think of something better but thought I would put it up here.

I have two lists, one of adjectives, one of nouns. I want somehow to generate every possible combination of the two. Eg:

List 1:

List2:
Noun1
Noun2
Noun3

gives us:

Is there a way to solve this problem using a macro or a pivot table?
NB ideally i would like all possible combinations to include reversals. i.e. 'Noun1&Adj1' and 'Adj1&Noun1' etc.

Matrix Combinations And Permutations
i've got 2 numeric numbers one in each cell. These numbers indicate Maximum occupancies for a hotel room...

3 5

The Occupancy table looks like this

Adults Children Infants... so taking the above numbers the table should be built up like this

1 0 0
2 0 0
3 0 0
1 1 0
1 2 0
1 3 0
1 4 0
1 1 1
1 1 2
1 1 3

3 2 0
3 0 2
3 1 1

etc...

so basically to room can have a maxium of 3 adults and 2 children equaling the maxium room occupancy.

i'm trying to create a function that will automatically do this and workout subsquent numbers below the maxmium but i can't get anywhere near the result i am looking for...

Unique Combinations/Permutations Of Words
I have a list for example:

apple
pear
grape
orange

i'm after some code that will create every possible combination of the list.

The examples i've found in the archives give all possible combinations of the same list in a different order

e.g apple, pear, orange, grape.......apple, orange, pear, grape.........apple, grape, orange, pear etc etc etc... THIS IS NOT WHAT I'M AFTER.

i'm after every possible combination starting right at the beginning with single words

e.g

apple
apple, pear
apple, pear, orange
apple, pear, orange, grape
pear, orange,
pear, orange, grape
orange,
orange, apple

etc etc you get the idea..... but i do not want repititions like

apple, pear.........pear, apple.
apple, orange, pear ...........pear, orange, apple.

Combinations/Permutations Of Words/Text
I'm trying to figure out how to generate all combinations from a list
of N values in a column, let's say column A. In particular, I want to have all combinations of 2 values, 3 values, 4, ... up to 7 values. To give an example: Let's assume I have a list of only 3 values (1,2,3) for which I want to have all combinations of two values. In this case, the result would be 1,2; 1,3; and 2;3. The ordering of the values does not matter, i.e. duplicates should be eliminated.

All Possible Combinations/Permutations Of Text Strings
I was just wondering is it possible that a excel spreadsheet could find all the different combinations for these set of letters. Also i can only have 1 letter from each group per combination.

First Group ABCDE

Second Group FGHIJK

Third Group LMNOP

Forth Group QRST

Anyone know is this is possible to create?

Permutations/Combinations For Column Relative To Groups In Another
I need to figure out how I can get excel to write me a list of permutations / combinations for the Group (column a) and Item (column b) columns in the example. The group designates the items that should be inlcuded in the combination / permutation in Related Items (column c). I have thousands of lines to do this with so I need to figure a way to automate it. I have started the Related Items column which is the results I need output. If it could format it like this adding in the space between the rows as it outputs the answer that would be perfect. Anyone know how to do this? I've found many answers, but none that have 2 columns with separate grouping within the column.

Number Combinations :: 25 Random Numbers (5 Digit Combinations)
I have 25 random numbers and I would like to get a possible 5 digit combinations of these numbers. Can anybody help me with the possible formula?

Permutations For Defined Numbers
I have a set of numbers 1-24, what I would like to have is to list every 4 set combination of 24 numbers. I believe this is 10626 combinations. I would like the combinations to display in seperate cells.

For example: Rows 1, column 1, 2, 3, and 4 would look like 1 2 3 4. No two numbers can be the same within that row. Row 2 would have 1 2 3 5 and so on untill all possible combinations are exhausted.

How does one do something like this within excel?

Also, I would like to be able to change the value of 24, so instead of entering 24 I could say I have a set of 32 and want a list of 4 or 3 permutable combinations. I want to be to make this as custom as possible.

Combinations From Set Of Numbers
I want to do all columns combination that is (C=4^N/(3*N+1); N=4) for numbers 1,2,3,4.

as like this,

1111....2222....3333.....4444.....
1111....2222....3333.....4444.....
1111....2222....3333.....4444.....
1234....1234....1234.....1234....

List All The Combinations Of A Group Of Cells Containing Letters, But Not Numbers
I have 7 cells containing strings but not numbers on a row.

Now I want to list out all the combinations of drawing out 3 cells out of these 7 cells while the remaining cells that haven't been drawn out could also be listed out one column next to the drawn cells.

For example, I got 7 cells like this.

A B C D E F G (each letter in ONE cell)

And I want to list out all the combinations like this:

ABC DEFG
ABD CEFG
ABE CDFG
ABF CDEG

etc.

For more details, please refer to the attached sample (an .xls file being zipped).

Number Combinations :: Between 7 To 15 (6 Digit Combinations)
What I am looking for is to select between 7 and 15 numbers in total, I want all the possible 6 digit combinations for this.

EG: if I choose 2,9,11,13,15,17&26, it would look something like this

2,9,11,13,15,17
2,9,11,13,15,26
9,11,13,15,17,26
And so on.

If I chose more numbers (10) 1,2,3,4,3,6,7,8,9,10 it would start something like this

1,2,3,4,5,6
1,2,3,4,5,7
1,2,3,4,5,8
1,2,3,4,5,9
1,2,3,4,5,10
And so on.

Please remenber I would like to be able to secelt between 7 and 15 number and be given all the possible combinations.

I would like it to be in one sheet but if that can not be done on as many as it takes.

It would be good if I could just type the required number into A1,B1,C1 and so on and they just gave the combinations required.

Permutations And Combinationns
I'm sure I should be able to do this but my brain is out of gear today!

Can someone tell me how I can create a list of every 5 letter permutation using only letters (A-D).

I also need to do the same for 4 letter and 3 letter, again using A-D.

Would prefer to do it without VB but if this is the only way......

Class Of Permutations
I am creating a class of permutations. The problem is that there are many ways to describe what a permutation does. for example.

Dim aPerm As New clsPermutation
Dim bPerm As New clsPermutation
aPerm.DoesTranspose(2,3) : Rem aPerm.Action({a,b,c}) = {a,c,b}
MsgBox (aPerm Is aPerm.Inverse)

I want the message box to return True. But since aPerm and aPerm.Inverse are different instances of clsPermutaion, it returns False. (.Inverse is a read-only property that returns a clsPermutation.). What I would like to do is have a collection, myPermutations. When I specify the action that aPerm does, I would like

1) if nothing in myPermutations does the same thing as aPerm, then add aPerm to myPermutations.

2) if something (xPerm) does the same thing as aPerm, then

Set aPerm=xPerm
so that "xPerm Is aPerm" returns True.
The problem I have is that in the class module,.....................

IF - FORMULA RESTRICTED TO 7 PERMUTATIONS
This formula will only do 7 permutations, I need it to do 8. Is there some way to do that? Thanks in advance.

=IF(AND(A10,B10),B10,(IF(AND(A10,B11),B11,(IF(AND(A10,B12),B12,(IF(AND(A10,B13),B13,(IF(AND(A10,B14),B14,(IF(AND(A10,B15 ),B15,(IF(AND(A10,B16),B16)))))))))))))

Permutations Checkspelling Speed
A1 has some characters
this code will generate all possible words, that can be made using all characters

system
permutate and checkspelling: if OK then write to column B

example
A1: iftrs
results: first frits rifts

Option Explicit

Dim CurrentRow
Const col = 2

Sub correctly_spelled_permutations()
Dim InString As String
Dim CalcSet As Integer
InString = Range("A1")
If Len(InString) < 2 Then Exit Sub

With Application
.ScreenUpdating = False
CalcSet = .Calculation
.Calculation = xlCalculationManual
.EnableCancelKey = xlErrorHandler
.StatusBar = "searching valid combination"....................

Formula Which Will Work Out 48 Permutations
I need to work out a formula which will work out 48 permutations.

There are three headings: Impact, Probability, Risk Category:

ImpactProbabilityRisk Category
VHM = 1
VHH = 1
VHVH = 1
HH = 1
HVH = 1
VHL = 2
HM = 2
MH = 2
MVH = 2
HL = 3
LVH = 3
MM = 4
LH = 4
ML = 5
LL = 5
LM = 5

The formula I need is: if Impact is "L" and probability is "M", then return answer = "5".

The thing is - there are 48 possible answers - and im not sure what formula you could type into 1 cell - which would answer this.

Permutations Of A List (groups Of 3)
Is there any way to determine all possible unique combinations (or sets) of any 3 strings in a table? I need to make a master set list from a list of strings which could be over 100 elements long.

Once I have a result set, I need to get rid of any groups which have a value contained in another group.

Example:
cells A1 through B100 contain:
Item1 45
Item2 50
Item3 98
...
Item100 75

Result set would contain groups of any 3 item combinations where the corresponding "B" value is within a certain range (between 40 and 80), while also trying to create sets with the lowest possible sum (placed in the 4th column) of the 3 numbers.

One possible combination would be:
Item1 Item2 Item100 170

etc...

I need to list all possible combinations, without re-using an element from a previous (lower sum) combination that matched the criteria.

Output Huge Number Of Permutations
I have several columns of info on my worksheet. I want to output a list of all possible permutations from this worksheet (not the number of permutations but the actual permutations themselves).

Permutations Function For Musical Notes
I need to find all 3, 4 and 5 letter permutations based on 5-8 musical notes as input. FYI the permutations will be chords. i.e. C, D, E, F, Ab, Bb, B as an input musical scale input would yield

All three note combos :
C,D,E
C,D,F
C, D, Ab
....
all 4 note combos
C,D,E,F
C,D,E,Ab

all 5 note combos
C,D,E,F,Ab
C,D,E,F,Bb
...

I'd like to structure the sheet as having 12 columns (1 for each note within an octave) with the combo placed under the right column i.e. C goes in 1, Eb in 4.

Count With Multiple Criteria And Find Permutations
I have a few calculations I cannot solve for life of me. I know you guys can figure this out. In the example attached you will see the list of the numbers that were drawn (More numbers will be added as time continues).

I was able to use " countif" to find the total number of time each number was drawn.
My delima, I need:

1. Count the number of times each number was drawn by person.

John starting in cell J7
Mary starting in cell J11

2. I need to type in 4 digits in cell J19, and find all possible combinations from the list of numbers drawn

List what combination of numbers that was drawn including the date it was drawn by person starting at cell I20 using the format as shown

All Possible Combinations That Sum Up To X
I have a column of transactions lets say 500 or so, of irregular numbers such as 257,273.80 (not something ou can add up in your head...). I know that of those 500 transactions a handful of them have a sum of lets say 2,877,000.00, which I know. Now I need to find all possible combinations of values in this column that equal a sum I enter.

Combinations Using Formula
I've attached an Excel..Its a small 4X4 matrix with numbers filled inside...Next to the right is a Combinations Column..I want to know how can i use just forumla to optain 4digit combination based on the 4X4 matrix. Rule is only numbers from the 4X4 be used.

Given Number Combinations
I want to have a sheet with all the previous drawings for the florida lottery.
Then I want excel to ask me how many numbers do I wish to play.

Then when I say 12 (for example) it would pick 12 numbers from 1 to 53 and match all possible comibinations of thoses numbers to the the previous drawings and tell me wich 12 number combination would have won more times then others. So it would need to compare each possible 12 nmber combination to each other and see wich one won more 6outof6, 5outof5, 4outof4, and 3outof3. Then give me the one with the highest winings

How To Calculate Combinations ?
I want to see how much combinations are possible when i got 6 numbers..

-- got this numbers 1--2--3--4--5--6
-- want to calculate how much combinations of ( 2 ) numbers possible
-- want to calculate how much of ( 3 ) numbers possible
-- want to calculate how much of ( 4 ) numbers possible
-- want to calculate how much of ( 5) numbers possible

-- never 2 same numbers together (2-2) or (2-2-3) or (2-2-3-4) may not be in list

-- How can i make the result visible in kind of list ?

I would be nice if somebody knows a good solution..

Figure Out The Combinations Available
i'm doing a process and in column N, i would need to have the following combinations:

A1
A2
C1
C2
H1
I1

so basically, a formula that would figure out the combinations available!
can this be done using a formula?

******** ******************** ************************************************************************>Microsoft Excel - Cost Calculator---V5---Try.xls___Running: 11.0 : OS = Windows XP (F)ile (E)dit (V)iew (I)nsert (O)ptions (T)ools (D)ata (W)indow (H)elp (A)boutK39=
KLMN39A12 40B 41C12 42D 43E 44F 45G 46H11 47I11 48J Cost Calculator
[HtmlMaker 2.42] To see the formula in the cells just click on the cells hyperlink or click the Name box
PLEASE DO NOT QUOTE THIS TABLE IMAGE ON SAME PAGE! OTHEWISE, ERROR OF JavaScript OCCUR.

Combinations Of Arrays Using Vba
I need to find the possible combinations for several arrays consisting of binary data. I shall give a simplified example with three arrays and four fields. Lets assume the three starting arrays look as follows:

1 0 0 0
1 0 0 0
1 0 0 0

Each row may contain one field = "1" and all other fields = "0". So the next possible combinations may be:

1 0 0 0
1 0 0 0
0 1 0 0

1 0 0 0
1 0 0 0
0 0 1 0

etc...until:

0 0 0 1
0 0 0 1
0 0 0 1

Assuming k = number of fields and c = number of arrays the possible combinations are k ^ c = 4 ^ 3 = 64. I am looking for vba coding that allows to cycle through all possible combinations and displays them in an excel spreadsheet. Ideally, the code should work for any k and c. Could anyone please give me any pointers as to how to tackle this problem?

p.s. in essence I'm looking for the tabular representation of a tree plan with four branches to commence with, a total of 16 decision nodes, and two possible outcomes (1 and 0)

Median Of All Combinations
I have 5 numbers (can be with decimals) in column A (A1:A5). For these
numbers, I want all combinations as well as the median of these
combinations.

I'm pretty far already. However, the median seems to be calculated
wrong.

Block Alt Key And All Combinations With It Except
This supposed to block Alt key and all combinations with it except Alt+F1, Alt+Tab and Alt+Shift. But what I get is: if I press Alt+F1 only, F1 is triggered.

Private Function LowLevelKeyboardProc(ByVal nCode As Long, _
ByVal wParam As Long, _
ByVal lParam As Long) As Long

Static kbdllhs As KBDLLHOOKSTRUCT

If nCode = HC_ACTION Then
Call CopyMemory(kbdllhs, ByVal lParam, Len(kbdllhs))
If CBool(kbdllhs.flags And LLKHF_ALTDOWN) Then
Select Case kbdllhs.vkCode
Case vbKeyF1, VK_LSHIFT, VK_TAB
Case Else
LowLevelKeyboardProc = 1
Exit Function
End Select
End If
End If
LowLevelKeyboardProc = CallNextHookEx(m_hDllKbdHook, nCode, wParam, lParam)
End Function

Display The Combinations
I have a list of numbers from 1 to 20 form a2 to a21, what I would like to do if possible if figure out many combinations of 5 there are for these numbers, and then second if possible display the combinations.

E.g. say there was a total 250000 combinations then show those 250000

Creating All Possible Combinations
I am trying to create a combination list. I have 48 items and I want to create all possible comibinations of 3 items from this group of 48 items.

I did something similar to create all possible combinations of 2 items from the group of 48 items in the attached spreadsheet. This was done manually and was time consumning. I want to do something similar for all possible combinations of 3 items from this group of 48 items.

All my 48 items are listed in rows 4 and 5. I want to enter the number "1" in each column to indicate my selection. Right now I have 2 ones per row. But I want to do 3 ones per row.

Generate All Possible Combinations
Is there an Excel Addin that will let me figure out the total number of combinations for any size number pool I specify (39,49, 53) and with any combination quantity I specify (3, 4, 5, 6)? And most important is that all these combinations be displayed in a column separated by commas.

Is a VBA script designed to handle something this complex.

Combinations - Win Or Draw
I'm creating a spreadsheet regarding football teams and want to lis thte combinations of results for each team.

Specifically, if the team will win or draw.

So, I have 6 teams, each team can either win or draw.

I want to display the combinations of team 1 winning AND team 2 winning AND team 3 winning etc.

Key Show All Of The Possible Combinations
Outside the door of my flat I have a key holder – which has a combination of 4 digits. No-one knows what the combination is, so I’d like to try to find it, clear it and use it.
I wondered if there was a way to use excel to show all of the possible combinations so I can then tick them off as I try them…?

The possible numbers are 0-9, but you cant press a button more than once in any given attempt… so… first possible combination would be 0123… not 0001.

Find Possible Combinations
I need to find possible combinations for the following example:

a*x + b*y + c*z = t
p = 10

Where
a = 0
b = 5
c = 10
t = 30

x + y + z has to = p

a, b, c, t, and p would be variables that I would specify. The numbers above are just examples. What I would need to see as output would be:

7a, 0b, 3c
4a, 6b, 0c
5a, 4b, 1c
etc...

Number Combinations
Here is what my table kind of looks like

A B
4 0.25
7 0.3
2 0.1
3 0.15

4 0.30
1 0.4
8 0.05
2 0.1

Now there is the number and the number(A) that it value it represents (B). This is what I want. I want to see all possible number combinations between the upper and lower A columns listed veritcally under the whole set, with out duplicating any numbers and with the upper numbers only being in the 1st position and the lower numbers being in the second position Ex( 4-1, 4-8, 4-2, 7-4, 7-1, ect, ect (listed vertically). Now in column B under, right beside each possible combination I want to see the result of the two values multiplied (ex. beside 4-1 I would like to see 0.1)

So below that mess listed above I want to see something like this

A B
4-1 0.1
4-8 0.0125
ect
ect
ect

I want to be able to swith the values around and have it automatically make the correction.

How To Count All Possible Combinations
I have a table:

And i need to count all possible combinatins. Result could be as:

Custome who use Voice also use combination:1VOICE ADSLCustome who use Data also use combination:1DATAIP2DATAADSLCustome who use IP also use combination:1IPDATACustome who use ADSL also use combination:1ADSLDATA

Permutation/Combinations
Can this be done in Excel? Using the digits 0,1,2,3,4,5,6,7,8,9 create all the permutations/combinations with limits on some of the digits. The digits 0,7,8,9 can only be used a max of 3 times in any one permutation/combination, digits 2,3,4,5,6 can only be used 4 time in any one permutaion/combination, producing a 5-digit string.
Example of expected results.
0 1 0 2 7

All Possible Combinations From Groups
I have a set of 13 groups, each with anywhere from 1-9 different variables for a total of 56 variables. I want to find all the possible combinations of 1-5 variables. Only one variable can be used from each group in a combination. Please see attached data sheet.

Combinations Which Are Exclusive Of Each Other
in columns CT, CU, and CV i have listed all possible combinations of 3 produced from the 12 variables (a through l). each combination has a score (listed in column cw). I have sorted all combinations in descending order by score. is there a way I can search all the combinations and select the 4 which have the highest score but are also exclusive? that is, none of the 4 combinations may contain the same variables.

Calculate All Possible Combinations
I have check list of 14games. With this I'd like to make combinations.

Each row has one default value for unchecked rows of 3 columns in the list.

Chart All Possible Combinations
I have 4 groups of 5 variables each. I need to know how to make a chart in excel that lists out all of the possible 4 variable combinations of each.

Example: The groups are Group A, grp B, Grp C, Grp D and each group has 5 variables. You can use one variable from each group for a combination.

Create A Table Of Combinations
I have a list of variables, each of which has an associated list of possible values. Simple example:

Fruit (apple, pear, peach)
Snack (Snickers, peanuts, crackers, pretzels)

Now, I need to build a table that for each line has every possible combination:

Fruit Snack
Apple Snickers
Apple Peanuts
Apple Crackers
Apple Pretzels
Pear Snack
Pear Snickers
Pear Peanuts
Pear Crackers
Pear Pretzels
Peach Snickers
Peach Peanuts
Peach Crackers
Peach Pretzels

My table will have over 18000 lines, so building it from scratch will take time...is there an easier way (I'm real rusty on VBA, so that would take a while just to figure out the syntax again).

Concatenating All Combinations From Two Lists
Column A has a list of items beginning in A2:
1
4
11
29
109
234

Column B has another list of items beginning in B2:
CAR
BOAT
TRUCK

Would like to put a list in column D, starting at D1, that concatenates both lists like this:
1CAR
1BOAT
1TRUCK
4CAR
4BOAT
4TRUCK
11CAR
11BOAT
11TRUCK
etc until all combinations have been covered.

Notes:
-Both lists can vary in number of items
-Both lists will never have a blank cell until the end of the list

I am thinking of a looping macro to do this, perhaps a loop within a loop? But I am stumped how to go about this.

I know this should be done in Access. but I need to do it in Excel.

Calculate The Combinations Of Entries
(I am unable to use Colo’s HTML Maker to post this—I have noticed several newer members indicating the same thing).

|....| 1 | 2 | 3 |4 | 5 | 6 | 7 | 8 |
| A | Y | N | Y | N | Y | Y | N | N |
| B | Y | N | N | Y | Y | N | N | N |
| C | Y | Y | N | Y | N | Y | Y | N |
| D | Y | Y | Y | N | Y | Y | N | Y |

The answer to the table above is: 144 combinations (using "Y" entries only). The answer is not to do just a simple count of the entries in each row and multiply as this produces 360 combinations rather than the desired 144 combinations. In this example, combinations such as 1-1-1-1 or 5-4-4-3 would not need to be calculated, which is the reason the answer is not 360 combinations.

The table always allows for 8 x 4 cell entries.
It is possible that every cell can be selected (the answer would be 8!/4! in this instance);
At least one entry must occur in each of the first 3 rows. In this example, if row 4 was excluded the answer would be 38 combinations (3 rows);

I am looking for 2 formulae: The first one to calculate the combinations of entries in 4 rows and the second to calculate for 3 rows only.

List Of All Possible Combinations Of The Integers
A user would input 4 integers.
How can I generate a list of all possible combinations of the integers?

Parking Charges Combinations
I have coins in the following denominations: 10 cents and 20 cents

IF my parking charge is 30 cents, I can pay the charge using:
a: 10 + 10 + 10 cents
b: 10 + 20 cents
c: 20 + 10 cents

= 3 combinations (a, b, c)
= 2 unique (a, b) or (a, c)

If my parking charge is 80 cents
What is the formula to use to find:
(i) The combinations (answer should be 34(?) posible combinations)
(ii) The unique combinations

whilst if the parking charge was 50 cents
Than there would be 8 possible combinations (as the answer to the formula!)