# Elementary Combinatorics Q

1. May 15, 2009

### blinktx411

1. The problem statement, all variables and given/known data
Suppose that a teacher wishes to distribute 25 identical pencils to Ahmed, Bar-
bara, Carlos, and Dieter such that Ahmed and Dieter receive at least one pencil
each, Carlos receives no more than ﬁve pencils, and Barbara receives at least four
pencils. In how many ways can such a distribution be made?

Or, in other words, find integer solutions to $$x_1 + x_2 +x_3+x_4=25, x_1>0, x_2>0, x_3\le5, x_4\ge4$$

I think the end result was like 132 or something.

Please let me know if i made any silly errors, but I'm more concerned that I made a fundamental error in the logic of this problem.

Edit: accidently hit some random buttons and it submitted wrong, the please see my other forum post titled "Elementary Combinatorics Q"

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