Track / Stage 4 / 180 of 340 #440 of 1964

Problem 440

AMC 12 late, AIME early

Combinatorics Difficulty 4.9 Find the answer

5. 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. Spacing, $ signs and \frac vs / are all fine.

Official solution

$36$

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