Olympiad Maths Prep

Track / Stage 4 / 232 of 340 #492 of 2000

Problem 492

AMC 12 late, AIME early
Combinatorics Difficulty 4.9 Find the answer

44. 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?

Official solution

44. Boys can sit on chairs with odd numbers in 5!=1205!=120 ways, and girls on chairs with even numbers in 4!=24-4!=24 ways. In total, we get 12024=2880120 \cdot 24=2880 ways.

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