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Topic: Counting Ways of Making Change for $1.00
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bacle

Posts: 838
From: nyc
Registered: 6/6/10
Counting Ways of Making Change for $1.00
Posted: Jan 11, 2013 2:02 AM
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Hi,

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?

Thanks.



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