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Suppose that I have 6 different books, 2 of which are math books. In how many ways can I stack my 6 books on a shelf if I do not want the math books to be at the ends?

 May 3, 2022
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You can choose two non-math books out and place them at the ends first, to ensure math books never will be at the ends.

 

Number of ways to choose two non-math books = \(\displaystyle\binom{6}{2}\).

But you have two ways to choose which book to place at the bottom, so you need to multiply 2.

 

Then, the remaining 4 books can be rearranged in any order in the middle, so multiply by another \(4!\), you get the total number of ways as \(720\).

 May 3, 2022

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