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Gnoma [55]
3 years ago
7

Cory is picking out some movies to rent, and he is primarily interested in comedies and horror films. He has narrowed down his s

elections to 14 comedies and 19 horror films. How many different combinations of 4 movies can he rent if he wants at least one comedy
Mathematics
1 answer:
densk [106]3 years ago
7 0

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

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