The library is to be given 3 books as a gift. The books will be selected from a list of 18 titles. If each book selected must have a different title, how many possible selections are there?

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Since the order of how the books are chosen is irrelevant, this is a combination problem.

The number of different selections is C(18,3) which is

`{18!}/{3!(18-3)!}`

`={18!}/{3!15!}`   simplify numerator

`={18 times 17 times 16 times 15!}/{3!15!}`  cancel common factors

`=3 times 17 times 16`

`=816`

There are 816 different possible selections of the book titles.

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