Track / Stage 4 / 68 of 340 #328 of 1964

Problem 328

AMC 12 late, AIME early

Combinatorics Difficulty 4.7 Find the answer

In how many ways can three people be selected for three identical positions from ten candidates?

Your answer

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

Official solution

Solution. According to formula (1.3.4), we find

$C_{10}^{3}=\frac{10!}{3!\cdot(10-3)!}=\frac{10!}{3!\cdot 7!}=\frac{10 \cdot 9 \cdot 8}{1 \cdot 2 \cdot 3}=120$

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