Ordering and serving meals randomly
Source: 2012 AIME I Problem 3
March 16, 2012
AMCAIMEsymmetry
Problem Statement
Nine people sit down for dinner where there are three choices of meals. Three people order the beef meal, three order the chicken meal, and three order the fish meal. The waiter serves the nine meals in random order. Find the number of ways in which the waiter could serve the meal types to the nine people such that exactly one person receives the type of meal ordered by that person.