Robert must read a few books from his home library. He read any 4 out of 6 books from the top shelf, and then any 2 out of 3 books from the middle shelf and then any 3 out of 6 books from the bottom shelf. In how many ways can Robert read the books, if different orders in which the books will be read count as different ways

Respuesta :

Answer:

Robert can read the books in 129,600 different ways.

Step-by-step explanation:

The order in which the book are read is important, which means that the permutations formula is used to solve this question.

Permutations formula:

The number of possible permutations of x elements from a set of n elements is given by the following formula:

[tex]P_{(n,x)} = \frac{n!}{(n-x)!}[/tex]

Top shelf:

4 books from a set of 6. So

[tex]P_{(6,4)} = \frac{6!}{2!} = 360[/tex]

Middle shelf:

2 books from a set of 3. So

[tex]P_{(3,2)} = \frac{3!}{2!} = 3[/tex]

Bottom shelf:

3 books from a set of 6. So

[tex]P_{(6,3)} = \frac{6!}{3!} = 120[/tex]

Total:

360*3*120 = 129,600

Robert can read the books in 129,600 different ways.