Question

Cory is picking out some movies to rent, and he is primarily interested in comedies and horror films. He has narrowed down his selections to 14 comedies and 19 horror films. How many different combinations of 4 movies can he rent if he wants at least one comedy

Answer 1

Answer:

37044 different combinations of 4 movies can he rent if he wants at least one comedy

Step-by-step explanation:

The order in which the movies are selected is not important, so we use the combinations formula to solve this question.

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 4 movies can he rent if he wants at least one comedy

The easier way to solve this is subtract the total from the number of combinations with no comedies.

Total:

4 movies from a set of 14 + 19 = 33. So

$C_{33,4} = \frac{33!}{4!(33-4)!} = 40920$

No comedies:

4 movies from a set of 19.

$C_{19,4} = \frac{19!}{4!(19-4)!} = 3876$

At least one comedy:

40920 - 3876 = 37044

37044 different combinations of 4 movies can he rent if he wants at least one comedy