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# Help

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In how many ways can I arrange 3 different math books and 5 different history books on my bookshelf, if I require there to be a math book on both ends?

Oct 15, 2019
edited by Guest  Oct 15, 2019
edited by Guest  Oct 15, 2019

#1
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There must be 2 math books on either side, and there are 3 to choose from, so there are 3 possible books for one end, and 2 for the other. Therefore there are 6 possible ways to arrange the books.

For every possible way to arrange the two math books at either end, there is a number of possibilities to sort the 1 math textbook and 5 history textbooks. Then to find the possible ways of arranging you would do 6! = 720

720 x 6 = 4320 ways to arrange the books

https://web2.0calc.com/questions/more-questions-halp has the same problem

Oct 15, 2019

#1
+1

There must be 2 math books on either side, and there are 3 to choose from, so there are 3 possible books for one end, and 2 for the other. Therefore there are 6 possible ways to arrange the books.

For every possible way to arrange the two math books at either end, there is a number of possibilities to sort the 1 math textbook and 5 history textbooks. Then to find the possible ways of arranging you would do 6! = 720

720 x 6 = 4320 ways to arrange the books

https://web2.0calc.com/questions/more-questions-halp has the same problem

Oofrence Oct 15, 2019
#2
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Thanks, Oofrence.....that was an excellent answer   !!!!   CPhill  Oct 15, 2019