Track / Stage 4 / 32 of 340 #292 of 1964

Problem 292

AMC 12 late, AIME early

Combinatorics Difficulty 4.6 Multiple choice

12. A magazine prints six photos, which are of three

famous people and their baby photos, but the three baby photos are not labeled as to which three people they belong to, and readers have to choose themselves. Assuming each photo is equally likely. Then the probability that a reader randomly selects three photos, making the baby photos correspond to the names of the three celebrities is:

Pick one

Official solution

12. B.

Let event $A$ be the event of correctly selecting three baby photos. Then $P(A)=\frac{1}{3!}=\frac{1}{6}$ .

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