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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 next to each other?

 Aug 4, 2021
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Ways to arrange the math books

1x1xxx       4 ways x 2 =8

1xx1xx        3 ways x2 6

1xxx1x        2 ways x 2 =4

1xxxx1         2 ways

                   total   20 ways      

                 the other three slots can be arranged amonsth the remaining 4 books in  4 * 3 * 2 *1 = 24 ways for each math book arrangement

 

20 * 24 = 480 ways

 Aug 4, 2021

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