Question

In how many ways can four French books, two Spanish books, and three German books are arranged on a shelf so that all books in the same language are together?

Answer 1

6

Answer 2

so you have the 3 diff groups that have to stay together -- F, S, and G so they can be arranged in order 3 x 2 x 1 = 6 diff ways
within each group you do the same thing --
4 F books can be arranged 4x3x2x1 =24 ways
2 S books: 2 x 1 = 2 ways
3 G books: 3 x 2 x 1 = 6 ways
so you have to multiply them all together to get total # of ways:
3!4!2!3! = ?

(remember that n! = n x n-1 x n-2 x ... x 3 x 2 x 1)