(a) Explain why the generating function for the number of ways to have n cents in pennies...

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(a) Explain why the generating function for the number of ways to have n cents in pennies and nickels is
(1 + x + x2 + x3 +------)(1 + x5 + x10 + ......).
(b) Find the generating function for the number of ways to have n cents in pennies, nickels, and dimes.
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