Generating Function (Kenneth Rosen)

Question

Ques #29 from Generating function

Use generating functions to find the number of ways to
make change for $\$100$ using
a) $\$10$, $\$20$, and $\$50$ bills.
b) $\$5$, $\$10$, $\$20$, and $\$50$ bills.
c) $\$5$, $\$10$, $\$20$, and $\$50$ bills if at least one bill of each denomination is used.
d) $\$5$, $\$10$ and $\$20$, bills if at least one and no more than four of each denomination is used.

Comments

https://math.stackexchange.com/questions/210404/generating-functions-help

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The generating function for the first part is

$ = (1+x^{10}+(x^{10})^2 + \dots)(1+x^{20}+(x^{20})^2 + \dots)(1+x^{50}+(x^{50})^2 + \dots)\\ = (\frac{1}{1-x^{10}}).(\frac{1}{1-x^{20}}).(\frac{1}{1-x^{50}}) $

here how do we find the coefficient of $x^{100}$.

Someone please comment

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https://gateoverflow.in/273761/generating-function