Probability, how many totals of 30... help plz!

On each play in a game any one of 5,4,3,2 or 1 can be scored. The number of combination of these scores which yield a total of 30 in 7 plays is.

If the total was somewhere in the middle (like 20) this would be complicated, but there actually aren't too many ways you can get 30 from 7 plays. So for each possible way, do the combinations, and then add them all up:

5555541 -> 7 * 6 ways
5555532 -> 7 * 6 ways
5555433 -> 7 * 6C2 ways
5555442 -> 7 * 6C2 ways
5554443 -> 7 * 6C3 ways
5544444 -> 7C5 ways

Where 6C2 = 6*5 / (2*1), 6C3 = 6*5*4 / (3*2*1) etc

I don't think I've missed any, but double check yourself :)

This is a problem on finding the number of partitions of 30 into 7 positive summands, each summand between 1 and 5 inclusive. Thoroughly explained in exercise 2.11 of this brochure: http://www.amazon.com/Discrete-Mathemati…