Difference between revisions of "2005 Alabama ARML TST Problems/Problem 12"
(New page: ==Problem== Find the number of ordered pairs of positive integers <math>(a,b,c,d)</math> that satisfy the following equation:<center><math>a+b+c+d=12</math>.</center> ==Solution== The [[G...) |
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Revision as of 21:15, 5 January 2008
Problem
Find the number of ordered pairs of positive integers that satisfy the following equation:
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 .