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I have 5 different biology textbooks and 4 different economics textbooks. In how many ways can I place the 9 textbooks on a bookshelf, in a row, if there must be an economics textbook in the middle, and there must be a biology textbook at each end?

 Apr 5, 2020
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I'm not the best at counting and probability problems, so don't get mad if I get this question wrong.

1. There are \(4*P{5 \choose 2}=240\) ways to place an economics text book in the middle as well as place a biology textbook at each end.

2. There are \(6!\) ways to arrange the remaining text books.

 

So \(720*240=172800\) total ways.

 Apr 5, 2020
edited by AnExtremelyLongName  Apr 5, 2020

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