Question 386163: If we are interested in determining how many different slates of officers (chairman, vice-chairman, and secretary) we can pick from a committee of five, would we apply the combination formula or the permutation formula? Explain. ( you don't have to actually do the computation).
Answer by solver91311(24713)   (Show Source):
You can put this solution on YOUR website!
Has to be a permutation. Permutations are calculated when the order of the elements in the selection matters. Combinations are calculated when the order of the elements in the selection doesn't matter.
Example: Let's say that you wanted to draw 5 cards from a standard deck of 52. As far as anyone is concerned 10♣, 9♠, 5♥, J♦, and A♠ is exactly the same as A♠, 10♣, 5♥, 9♠, and J♦. The order in which the cards were drawn makes no difference. That means if you calculated the Permutations of 5 taken from 52 and there are 5! ways to arrange your selection of 5, the answer would be 5! = 120 times too large. Hence, you would use the Combination calculation which differs from the Permutation calculation by a factor of 5! in the denominator.
Your example: Picking a slate of officers is a very different thing. Consider that President Obama, Vice-President Biden, and Secretary of State Clinton is a vastly different result than President Clinton, Vice President Obama, and Secretary of State Biden. Order matters, so use a Permutation.
Capisce?
John
My calculator said it, I believe it, that settles it
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