Mock AIME 4 2006-2007 Problems/Problem 8

Problem

The number of increasing sequences of positive integers $a_1 \le a_2 \le a_3 \le \cdots \le a_{10} \le 2007$ such that $a_i-i$ is even for $1\le i \le 10$ can be expressed as ${m \choose n}$ for some positive integers $m > n$ . Compute the remainder when $m$ is divided by 1000.

Solution

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Mock AIME 4 2006-2007 Problems/Problem 8

Problem

Solution