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2006/07 AHSMC Part 1 Problem 5

Problem 5 of 16

When (1+x)(1+x2)(1+x3)(1+x4)(1+x5)(1 + x)(1 + x^2)(1 + x^3)(1 + x^4)(1 + x^5) is expanded, the coefficient of the term x9x^9 is

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Solution

We are counting the number of ways of making 99 from 11, 22, 33, 44 and 55, using each number at most once. There are 33 ways, namely 1+3+51 + 3 + 5, 2+3+42 + 3 + 4 and 4+54 + 5. The answer is (d).

University of Alberta