MathMaster logo

MathMaster

  1. Home
  2. general
  3. rafael is picking out some movies to rent and he is primarily interested in documentaries and foreign films he has narrowe
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

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
88 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)
What is the possible value of x to make triangles ΔABC and ΔPQR congruent? AB = 5x + 4, BC = 3x + 7, QR = 4x + 16.
+
John collects data on the number of hours he spends studying each day. If he studies for 4, 2, 3, 5, and 6 hours on the first five days, what is the average number of hours he studies?
+
What is the smallest positive integer solution for the equation x^n + y^n = z^n, where x, y, z, and n are positive integers? (
+
New questions in Mathematics
How to find the value of x and y which satisfy both equations x-2y=24 and 8x-y=117
a ferry travels 1/6 of the distance between two ports in 3/7 hour. The ferry travels at a constant rate. At this rate, what fraction of the distance between the two ports can the ferry travel in one hour.
What is the amount of interest of 75,000 at 3.45% per year, at the end of 12 years and 6 months?
A hotel in the Algarve had to offer 1 week of vacation to one of its employees as an Easter gift in a random choice. It is known that 80 people work in this hotel unit, 41 of whom are Portuguese and 39 are foreign nationals. There are 14 Portuguese men and 23 foreign women. Using what you know about conditional probability, check the probability that the gift was offered to a Portuguese citizen, knowing that it was a woman.
A food delivery company charges on average a delivery fee of $5 per order (including food and shipping) and has monthly fixed costs of $600. If the average cost of each meal delivered that is revenue for the company is $10 and the company has a monthly profit of $800, how many orders must they deliver per month?
The sum of two numbers is 6, and the sum of their squares is 28. Find these numbers exactly
The director of a company must transfer 6 people from the human resources department to the sales department, in order to sustain sales during the month of December. What is the probability that he will transfer only 2 of them?
An integer is taken at random from the first 40 positive integers. What is the probability that the integer is divisible by 5 or 6?
A force of 750 pounds compresses a spring 3 inches from its natural length, which is 15 inches. What will be the work done to compress it 3 inches more?
solve for x 50x+ 120 (176-x)= 17340
Prove that it is not possible to arrange the integers 1 to 240 in a table with 15 rows and 16 columns in such a way that the sum of the numbers in each of the columns is the same.
How to do 15 x 3304
Three machines called A, B and C, produce 43%, 26% and 31% of the total production of a company, respectively. Furthermore, it has been detected that 8%, 2% and 1.6% of the product manufactured by these machines is defective. a) What is the probability that a product is not defective? b) A product is selected at random and found to be defective, what is the probability that it was manufactured on machine B?
User One of the applications of the derivative of a function is its use in Physics, where a function that at every instant t associates the number s(t), this function s is called the clockwise function of the movement. By deriving the time function we obtain the velocity function at time t, denoted by v(t). A body has a time function that determines its position in meters at time t as S(t)=t.³√t+2.t . Present the speed of this body at time t = 8 s.
Twenty‐five students in a class take a test for which the average grade is 75. Then a twenty‐sixth student enters the class, takes the same test, and scores 70. The test average grade calculated with 26 students will
2X+2=8
Associate each 2nd degree equation with its respective roots. A) x2+6x+8=0 B)x2-5x-6=0
a) Statistics scores are normally distributed with the mean of 75 and standard deviation of 7. What is the probability that a student scores between 80 and 88
How many digits are there in Hindu-Arabic form of numeral 26 × 1011
A small box measures 10 in. by 4 in. by 6 in. high. Find the volume of the box.

You might be interested in