Question: find a generating function for the number of ways to distribute n identical juggling balls to five different jugglers if each juggler receives at most seven balls. And then compute how many ways 25 balls can be distributes with the generating function.
This what I think the generating function is: (1 + Z^1 + Z^2 ..... + z^7)^5
And then for the numbers of ways 25 balls can be distributed in the manner as stated in the question would be: 14Cr10
Are my answers correct?