Multiple choice

A supervisor wants to assemble a 7-person task force from 12 available candidates. She has already selected 4 members. How many different combinations of the remaining 3 candidates can be selected to complete the task force?

  1. 10

  2. 20

  3. 56

  4. 84

  5. 120
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Since 4 members of the 7-person task force have already been selected from the 12 candidates, the supervisor needs to choose 3 more members from the remaining 8 candidates. The number of ways to do this is given by the combination formula 8C3 = (8 * 7 * 6) / (3 * 2 * 1) = 56.

AI explanation

Since 4 members are already selected, the supervisor must choose the remaining 3 members from the 8 available candidates. We apply the combination formula nCr to find the number of ways to make this selection. This gives 8C3 = 8! / (3! x 5!) = (8 x 7 x 6) / (3 x 2 x 1) = 56 combinations.

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