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In how many ways can a President and a Vice-President and a Treasurer be chosen from a group of 5 people (assuming that the President and the Vice-President and the Treasurer cannot be the same person)?

 Feb 28, 2022
 #1
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5 choices for first position

   4 choices remain for second position

       3 choices remain for third position                         5  x  4  x 3  = _________   ways

 Feb 28, 2022
 #2
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I suppose the order doesn't matter, so I'd expect the answer to rather be 5C3 (5 choose 3 and not 5 permute 3), which gives 5!/(2!*3!) = 10 ways.

 Feb 28, 2022

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