Track / Stage 4 / 192 of 340 #452 of 1964

Problem 452

AMC 12 late, AIME early

Combinatorics Difficulty 4.9 Find the answer

Three ants, Xiaohong, Xiahei, and Xiaohuang, go on a trip. The hotel has 9 different rooms, and no two ants can stay in rooms that are in the same row or the same column. There are $\qquad$ possible arrangements for their rooms.

Your answer

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

Official solution

$36$

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