Track / Stage 4 / 128 of 340 #388 of 1964

Problem 388

AMC 12 late, AIME early

Combinatorics Difficulty 4.8 Find the answer

In a certain sports competition, the scoring rules are: 3 points for a win, 1 point for a draw, and 0 points for a loss. If a player competes in 15 matches, then the number of ways to score a total of 22 points is ( ).
A. 3 ways
B. 4 ways
C. 5 ways
D. 6 ways

Your answer

Multiple choice: answer with the letter of the option you want.

Official solution

9. B. Since the number of wins must be no less than 4 and no more than 7, the four scenarios are: the number of wins, draws, and losses are $4,10,1 ; 5,7,3 ; 6,4,5 ; 7,1,7$ .

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