A residents' welfare committee of 3 men and 2 women is to be formed from 6 men and 5 women who have volunteered. In how many ways can the committee be formed?

30Correct answerYour answer200Correct answerYour answer462Correct answerYour answer2,400Correct answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer B

Correct answer: B

Men: ${}^{6}C_{3} = 20$ ways. Women: ${}^{5}C_{2} = 10$ ways.
Both choices are needed together, so multiply: $20 \times 10 = 200$ .

Worth noting

30 adds $20 + 10$ ; the committee needs the men AND the women. 462 is ${}^{11}C_{5}$ , which ignores the 3-and-2 split. 2400 uses permutations, but committee members have no order.

Concept: Selecting from two groups with the multiplication rule
Typical timeTypical: 70 s
Your timeYours: —

The rule this testsArrangements and selections

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Ten questions from Counting and Basic Probability, at your own pace.

A residents' welfare committee of 3 men and 2 women is to be formed from 6 men and 5 women who have volunteered. In how many ways can the committee be formed?

Explanation