We can use multinomials to find the number of ways of making change for $1.00 with standard coins with values: 1,5,10 and 25 cents respectively . We take:
(1+x+x^5+ x^10+ x^25 )^100
And find the coefficient of x^100 in the expansion.
Question(s): Is there a nice, relatively-short way of finding the coefficient of x^100 in the expansion? Is there another nice way , without multinomials/generating functions to count the number of ways?