I have 5 different latin textbooks and 4 different geography textbooks. In how many ways can I place the 9 textbooks on a bookshelf, in a row, if there must be a geography textbook in the middle, and there must be a latin textbook at each end?
We have 4 ways to choose the geography book to occupy the middle position
And we have C(5,2) = 10 ways to choose the latin textbooks.....and each of these can be arranged in 2 ways
And the other textbooks can be arranged in 6! = 720 ways
So....the total arrangements =
4 * C(5,2) * 2 * 720 =
4 * 10 * 2 * 720 =
57,600 possible arrangements