HMMT February

Combinatorics Difficulty 5.0 AIME Find the answer

Count the number of sequences $1 \leq a_{1} \leq a_{2} \leq \cdots \leq a_{5}$ of integers with $a_{i} \leq i$ for all $i$ .

Your answer

A number or a short expression. Fractions can be typed as 3/2, and spacing doesn't matter.

Solution

$C$ (number of terms) $=C(5)=42$ .

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Source: Omni-MATH, licensed Apache-2.0. Statement reproduced verbatim; metadata (topic, difficulty) added by this project.