Probability Combinations Of Events Occuring

I need a probability distribution for amounts to be shipped taking into account both the probabilty distribution on parcel sizes (amounts to be shipped) per ship as well as the probabilities on the number of ships arriving.

Please see the following:

Say you have a probabilty distribution for ships arriving, i.e. the probabilty of 1 ship arriving in a specific time period= 0.25 ( event a), the probabilty of 2 ships arriving = 0.2 (event B) etc. Please take into account that this can go up to about 20 ships per time period.

Each ship can have one of four parcel sizes, (demand that needs to be met) (the following are just example probabilties)

0 tons with a probability of 0.67 event 1
1000 tons with a probabilty of 0.08 event 2
1500 tons with a probabilty of 0.222 event 3
2000 tons with a probabilty of 0.022 event 4

Thus event a has a probabilty of occuring, in event a, events 1to 4 can occur with their respective probabilties.

I assumed events 1 to 4 stay the same for all ships arriving (as we are dealing with multiple products, each product will have different parcel size distributions, however I look at products seperately, thus only one product is considered here)

This is simple for 1 or 2 ships, but as the number of ships increase the number of combinations become excessively large.

Should i use a macro that determines permutations/combinations? I am kind of clueless on this one.

If it helps to put the problem in context; I am trying to determine a demand distribution as input for a stochastic programming model