Competition problem — Combinatorics

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Combinatorics Difficulty 2.6 Junior Find the answer

Select 3 volunteers from 6 boys and 2 girls, where there is at least 1 girl among the volunteers. The total number of ways to do this is

Pick one

Solution

To select 3 volunteers from 6 boys and 2 girls, there are a total of $C_{8}^{3}$ ways. This includes selections that do not meet the requirement of having at least one girl, which are the selections with only boys. The number of ways to select 3 volunteers with only boys is $C_{6}^{3}$ . Therefore, the number of ways to select 3 volunteers with at least 1 girl is $C_{8}^{3} - C_{6}^{3} = 56 - 20 = 36$ . Hence, the correct answer is $\boxed{B}$ .

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