Question

There are 4 different French books and 4 different Spanish books. How many ways are there to arrange them on a shelf if

(a) Books of the same language must be grouped together, French on the left, Spanish on the right?

(b) French and Spanish books must alternate in the grouping, beginning with a French book? ...?

Answer 1

(a) Books of the same language must be grouped together, French on the left, Spanish on the right

Answer 2

a.) Number of ways the French books will be arranged in the left = 4! = 4 x 3 x 2 x 1 = 24
b.) Number of ways the Spanish books will be arranged = 4! = 24
Number of ways of arranging the books such that the same language must be grouped together French on the left and Spanish on the right are 24 x 24 = 576 ways.

b.) Number of ways af arranging the books such that the books alternate beginning with a French book = 4 x 4 x 3 x 3 x 2 x 2 x 1 x 1 = 24 x 24 = 576 ways.