Track / Stage 4 / 240 of 340 #500 of 1964

Problem 500

AMC 12 late, AIME early

Combinatorics Difficulty 4.9 Find the answer

Boys and girls sit on chairs numbered from the first to the ninth, with 5 boys and 4 girls sitting down. Boys sit on chairs with odd numbers, and girls sit on chairs with even numbers. In how many ways can this be done?

Your answer

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

Official solution

44. Boys can sit on chairs with odd numbers in $5!=120$ ways, and girls on chairs with even numbers in $-4!=24$ ways. In total, we get $120 \cdot 24=2880$ ways.

Source: NuminaMath-1.5, licensed Apache-2.0. Statement reproduced verbatim; metadata (topic, difficulty, ordering) added by this project.