Difference between revisions of "2005 Alabama ARML TST Problems/Problem 12"
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Revision as of 21:16, 5 January 2008
Problem
Find the number of ordered pairs of positive integers that satisfy the following equation:
![$a+b+c+d=12$](http://latex.artofproblemsolving.com/c/e/6/ce6136616ccd8c46acf5b3c5add0fcd7203037b3.png)
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 .
See Also
2005 Alabama ARML TST (Problems) | ||
Preceded by: Problem 11 |
Followed by: Problem 13 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 |