distributing k pennies to n children

Question

there are 100 pennies and 10 children

every child can get either 5, 10 or 20 pennies

How many ways to do in this case?

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I assumed that n = pennies, and k = children

so if first child can get 5, 10 or 20 pennies which is n-5, n-10, or n-20

if I keep going like that, It feels like i am counting all possibilities.

I just don't know how to approach and solve this question.

Answer 1

Consider the expansion of $(x^5 + x^{10} + x^{20})^{10}$. The result you want will be the coefficient of $x^{100}$ in the expansion.

Wolfram Alpha says it is $\boxed{4351}$.