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Why does a!/(a-b)! give the number of combinations?

Say you had a people on a train, and b train stations. If no more than 1 person got off at each station, and the train was empty by the last stop, why would the number of ways that people could leave the train be given by a!(a−b)!\dfrac{a!}{(a-b)!}?
Original post by Brian Moser
Say you had a people on a train, and b train stations. If no more than 1 person got off at each station, and the train was empty by the last stop, why would the number of ways that people could leave the train be given by a!(a−b)!\dfrac{a!}{(a-b)!}?


Is it?

I would have thought it was b! In the numerator

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