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?
+23254 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.
