Respuesta :
Answer:
There are 3,659,040 ways he can choose the books to put on the list.
Step-by-step explanation:
There are
12 novels
8 plays
12 nonfiction.
He wants to include
5 novels
4 plays
2 nonfiction
The order in which the novels, plays and nonfictions are chosen is not important. So we use the combinations formula to solve this problem.
[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
How many ways can he choose the books to put on the list?
Novels:
5 from a set of 12. So
[tex]C_{12,5} = \frac{12!}{5!7!} = 792[/tex]
Plays:
4 from a set of 8. So
[tex]C_{8,4} = \frac{8!}{4!4!} = 70[/tex]
Nonfiction:
2 from a set of 12
[tex]C_{12,2} = \frac{12!}{2!10!} = 66[/tex]
Total:
Multiplication of novels, plays and nonfiction.
[tex]T = 792*70*66 = 3,659,040[/tex]
There are 3,659,040 ways he can choose the books to put on the list.
