Question

Suppose you have six different books on a shelf with labels A, B, C, D, E, and F. (a) In how many different ways can you arrange the books on the shelf? In other words, how many distinct linear permutations of these are possible? (b) In how many different ways can you arrange the books on the shelf if books A, B, and C are grouped together? For example, EBACFD would be an acceptable arrangement, but EBAFDC would not be an acceptable arrangement.

Answer 1

Total books on the shelf = 6

a) Total number of permutations possible = 6P6 = 6! / (6 - 6)! = 6! = 720

b) Let's assume ABC to be as a single book. So in total there will be 4 books. Total number of ways to arrange these 4 books 4!. And the 3 books ABC which we assumed as a single book can be rearranged among themselves in 3! ways.

Total number of different arrangements = 4! * 3! = 144