Question

Giovanni is picking out some movies to rent, and he has narrowed down his selections to 5 comedies, 6 children's movies, 4 dramas, and 5 mysteries. How many different combinations of 9 movies can he rent if he wants all 6 children's movies?

Answer 1

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:

$C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

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

$T = C_{6,6}*C_{14,3} = \frac{6!}{0!6!}*\frac{14!}{3!11!} = 364$

There are 364 different combinations of 9 movies can he rent if he wants all 6 children's movies.