2005 Alabama ARML TST Problems/Problem 12
Problem
Find the number of ordered pairs of positive integers that satisfy the following equation:
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Solution
The Generating Function for a is . The same for b, c, and d.
Since the existance of the Binomial Theorem, we can assume that these are the results of choosing.
Checking , it works.
We want the coefficient of x^12, so we have .