Question

Suppose there are nine different English books, seven different French books, and five different German books on a bookshelf. How many rearrangements of these books will have all five German books next to each other?

A) (9! x 7! x 5!)
B) (5! x 9! x 7!)
C) (9! x 5! x 7!)
D) (7! x 5! x 9!)

Answer 1

The number of rearrangements with all five German books next to each other is calculated by multiplying the number of arrangements of the German, English, and French books separately.

Step-by-step explanation:

To find the number of rearrangements of the books that have all five German books next to each other, we can treat the five German books as a single entity. Therefore, there are 5! (the number of arrangements of the German books) x 9! (the number of arrangements of the remaining English books) x 7! (the number of arrangements of the French books).

Thus, the correct answer is option C) (9! x 5! x 7!).