A softball team with 13 players shows up for a game. By choosing players from the 13 participants, how many different ways are there to distribute the 10 positions?

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cyhuddwyr9 · Accepted Answer

We are interested in the number of subsets with an odd number of elements from a set with 10 elements. n=13 r=10 The order in which the players are selected matters, as a different order of the players results in the different players having different positions, and thus we should use the definition of a permutation. Number of ways =P(13,10) =13!(13−10)! =13!3! =13⋅12⋅11⋅10⋅9⋅8⋅7⋅6⋅5⋅4⋅3⋅2⋅13⋅2⋅1 =13⋅12⋅11⋅10⋅9⋅8⋅7⋅6⋅5⋅4 =1,037,836,800 Thus there are 1,037,836,800 ways to assign the 10 positions.

Thirteen people on a softball team show up for a game. How many ways are there t

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