Question 676713: 3 of 6 people are going to be chosen for a committee. The positions on the committee will be chair, secretary, and treasurer. In how many different ways can three positions be filled?
My answer: 6r3 = 20
Answer by solver91311(24713)   (Show Source):
You can put this solution on YOUR website!
Your answer works if you were just filling three committee member positions, so the order in which the positions were filled would not matter. But in the given situation, Billy (chair), Tommy (Secretary), Suzy (Treasurer) is a different outcome than Suzy (chair), Billy (Secretary), Tommy (Treasurer).
So, instead of the number of combinations of 6 things taken 3 at a time, you nee the number of permutations of 6 things taken 3 at a time. The difference is a factor of 3! in the denominator of the combination formula that is not present in the permutation formula. Multiply your answer by 6.
John
Egw to Beta kai to Sigma
My calculator said it, I believe it, that settles it
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