Respuesta :
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:
[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 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
[tex]C_{33,4} = \frac{33!}{4!(33-4)!} = 40920[/tex]
No comedies:
4 movies from a set of 19.
[tex]C_{19,4} = \frac{19!}{4!(19-4)!} = 3876[/tex]
At least one comedy:
40920 - 3876 = 37044
37044 different combinations of 4 movies can he rent if he wants at least one comedy
