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

 Jan 26, 2020
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There are 4 ways to select a science textbook to in the middle. (There are now 3 science books remaining.)

There are 5 ways to select a history textbook to place a on the left-hand end. (There are now 4 history books remaining.)

There are 4 ways to select a history textbook to place on the right-hand end. (There are now 3 history books remaining.)

 

With 6 books remaining, you can fill the other 6 spaces in 6 x 5 x 4 x 3 x 2 x 1 ways.

 

The total number of ways is:  4 x 5 x 4 x 6 x 5 x 4 x 3 x 2 x 1 ways.

 Jan 26, 2020

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