## General Question

# Why doesn't this work (combinations and permutations)?

There is a group of 13 people and you are to choose 10 of them (order doesn’t matter) – trivially, this is 13C10 = 286.

Now say 3 of the people are women and you are to choose a team that includes at least one woman. This is equal to the total number of groups minus the one grouping that is only men, 285.

Another way I thought about the problem doesn’t yield the right answer even though it seems to make sense. It goes as follows: choose one woman to include on the team – 3C1 – then choose any grouping of the remaining people – 12C9. Multiply and get 660, which is obviously wrong because it’s larger than the number of possible teams even when you place no restrictions on your choice-making parameters.

Why is this method wrong?

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