Respuesta :
Answer:
There are 364 different combinations of 9 movies can he rent if he wants all 6 children's movies.
Step-by-step explanation:
The order is not important.
For example watching drama movie A and then drama movie B is the same combination as watching drama movie B then drama movie A. So we use the combinations formula to solve this problem.
Combinations formula:
[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 different combinations of 9 movies can he rent if he wants all 6 children's movies?
There are 5 + 6 + 4 + 5 = 20 movies
He will pick 6 of 6(all of the children movies) and 3 of the other 20-6 = 14. So
[tex]T = C_{6,6}*C_{14,3} = \frac{6!}{0!6!}*\frac{14!}{3!11!} = 364[/tex]
There are 364 different combinations of 9 movies can he rent if he wants all 6 children's movies.
