How many ways to eat 10 donuts with 5 different flavors?

Question

How many ways are there to select 10 donuts with 5 different flavors? Note that it is not necessary to include all 5 flavors in 1 selection. Write your answer as the coefficient of $x^n$ (for some $n$) of a power series in rational form. Each selection of donuts are different from the rest.

Please help :(

-1. Please, try to show us you what you did and where you are in troubles. — Sigur, Jul 02 '13 at 00:40
I am thinking that the answer should be $x^n$^10 but it is probably wrong. — Robert McDonald, Jul 02 '13 at 00:41

score 1 · Answer 1 · answered Jul 02 '13 at 00:49

1

Hint: Consider $f_i$ the number of donuts of flavor $i$, for $i=1,\ldots,5$. So you have to determine the number of solutions of $f_1+f_2+f_3+f_4+f_5=10$, with $0\leq f_i\leq 10$.

answered Jul 02 '13 at 00:49

Sigur

6,416
3
25
45

Thank you for the hint. I have been working on this for a bit, and I still can't seem to get the answer for this. HOw would I arrive at $[x^n]$(some function)? – Robert McDonald Jul 02 '13 at 14:26
1

I think I have got it now. Thanks for your help :) – Robert McDonald Jul 02 '13 at 14:44

How many ways to eat 10 donuts with 5 different flavors?

1 Answers1