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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lfryerda
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calendarEducator since 2012
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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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