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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?

 May 8, 2020
 #1
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There are 4*P(5,2) = 240 ways to place an economics text book in the middle as well as place a biology textbook at each end.  There are 5! = 120 ways to arrange the remaining textbooks.

 

So the answer is 240*120 = 28800.

 May 8, 2020
 #2
avatar+109519 
+1

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?

B1 B2 B3 B4 B5     E1 E2 E3 E4

 

B***E***B 

 

5 * 4 * 4 * 6! = 57600   

 May 8, 2020

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