Track / Stage 4 / 60 of 340 #320 of 1964

Problem 320

AMC 12 late, AIME early

Combinatorics Difficulty 4.7 Multiple choice

1. Given the set $M=\{1,2, \cdots, 10\}, A$ is a subset of $M$ , and the sum of the elements in $A$ is 8, then the number of subsets $A$ that satisfy the condition is

Pick one

Official solution

The choices for $A$ are $\{8\},\{1,7\},\{2,6\},\{3,5\},\{1,2,5\},\{1,3,4\}$ , a total of 6, so the answer is $C$ .

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