Question

Rafael is picking out some movies to rent, and he is primarily interested in documentaries and foreign films. He has narrowed down his selections to 16 documentaries and 15 foreign films. How many different combinations of 4 movies can he rent if he wants at least one documentary?

82

likes411 views

Madelyn

4.7

53 Answers

To determine how many different combinations of 4 movies Rafael can rent with at least one documentary involved, we can use the concept of combinations from combinatorics. The total number of ways to choose 4 movies from 31 total films (16 documentaries and 15 foreign films) is one part of the calculation.
However, since Rafael wants at least one documentary, we should exclude the combinations where there are no documentaries at all. So, first, we calculate the total number of ways to pick any 4 movies, then subtract the number of ways to choose 4 movies that are all foreign films.
Let's do the calculations step by step:
1. Calculate the total number of combinations of 4 movies he can rent from 31 films.
2. Calculate the number of combinations of 4 movies he can rent that are all foreign films.
3. Subtract the all-foreign-film combinations from the total combinations to get the number of combinations with at least one documentary.
Rafael can rent 30,100 different combinations of 4 movies if he wants at least one documentary among his selections.

Frequently asked questions (FAQs)

Math Question: What is the limit of (cos(2x) - 1)/(x^2), as x approaches 0?

+

What is the sine ratio of an angle in a right triangle if the opposite side is 4 and the hypotenuse is 5?

+

Question: What is the formula for finding the median of a data set and how does it relate to the number of data points?

+

New questions in Mathematics