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?

Name: Solved: 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? - MathMaster
Brand: MathMaster
Rating: 4.9 (82 reviews)

likes

411 views

Answer to a math 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?

$Expert avatar$

Madelyn

4.7

86 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)

Find the integral of ∫(2x^3 - 5x^2 + 3x + 4)dx using the power rule.

Question: Find the value of sin(60°) + cos(45°) × tan(30°)

Math question: Find the measure of angle BAD in a circle, given that angle ABD is 70 degrees and BAD intersects the diameter at point C.

New questions in Mathematics

A circular park has a diameter of 150ft. A circular fence is to be placed on the edge of this park. Calculate the cost of fencing this park if the rate charged is $7 per foot. Use π = 3.14.

I) Find the directional derivative of 𝑓(𝑥, 𝑦) = 𝑥 sin 𝑦 at (1,0) in the direction of the unit vector that make an angle of 𝜋/4 with positive 𝑥-axis.

Express the following numbers in decimal system, where the subscript indicates the base: 110101 (SUBINDEX=2)

Consider numbers from 1 to 2023. We want to delete 3 consecutive, so that the avarage of the left numbers is a whole number. How do we do that

Solve the math problem 400 students are asked if they live in an apartment and have a pet: Apartment: 120 Both: 30 Pet: 90 The probability that a randomly selected student not living in an apartment has a pet is

what is the annual rate on $525 at 0.046% per day for 3 months?

During a fishing trip Alex notices that the height h of the tide (in metres) is given by h=1−(1/2)*cos(πt/6) where t is measued in hours from the start of the trip. (a) Enter the exact value of h at the start of the trip in the box below.