Competition problem — Combinatorics

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Combinatorics Difficulty 4.7 AIME Find the answer

9. The number of integer solutions greater than 1 for the equation $x+y+z=24$ is

Your answer

A number or a short expression. Spacing and $ signs are ignored.

Solution

9. 190 The problem is equivalent to finding the number of non-negative integer solutions to $x^{\prime}+y^{\prime}+z^{\prime}=18$ . According to the conclusion of question 7, the number is $C 18+3-1=C a_{0}=190$ .

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Source: NuminaMath-1.5, licensed Apache-2.0. Statement and solution reproduced as published; topic and difficulty added by this site.