Rand Pick From 4 Pools

I have been using the RAND and Vlookup functions for the following without success.

I have 4 numeric Pools or Groups;
1. A1:A18 (1-18)
2. B1:B18 (19-36)
3. C1:C17 (37-53)
4. D1:D17 (54-70)

I also have E1:E20 (20 existing Numbers from 1-70)

I want Excel to select at random a total of 20 numbers
and place them in F1:F20.

I will specify a quantity from each of the 4 groups.
Eg.
In cell A20 I enter 4 to obtain 4 numbers from grp 1,
In cell B20 I enter 6 to obtain 6 numbers from grp 2,
In cell C20 I enter 8 to obtain 8 numbers from grp 3,
In cell D20 I enter 2 to obtain 4 numbers from grp 4,

However there must not be any duplicates between
E1:E20 and F1:F20!