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
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)
Math Question: What is the fifth-order derivative of f(x) = 3x^4 + 2x^3 - 5x^2 + 7x - 1?
+
Math question: In ΔABC and ΔDEF, if ∠A = ∠D, AB = DE, and BC = EF, then prove that ΔABC ≅ ΔDEF using which rule?
+
What is the maximum value of the function f(x) = 2x^3 - 12x^2 + 16x on the interval [-2, 6]?
+
New questions in Mathematics
A=m/2-t isolate t
X^2 = 25
[(36,000,000)(0.000003)^2]divided(0.00000006)
Analyze the following situation Juan is starting a new business, he indicates that the price of his product corresponds to p=6000−4x , where x represent the number of tons produced and sold and p It is given in dollars. According to the previous information, what is the maximum income that Juan can obtain with his new product?
According to a survey in a country 27% of adults do not own a credit card suppose a simple random sample of 800 adults is obtained . Describe the sampling distribution of P hat , the sample proportion of adults who do not own a credit card
You mix a powder drug with a 4.5ml of liquid to get a reconstituted solution with a concentration of 250mg/ml. The prescribers order is for 500 mg . You will give what ml of the reconstituted solution
User The average height of Aranka, Böske, Cili, Delinke and Lili is 172 cm. We know that Aranka and Cili are both 172 cm tall. The sum of the heights of Böské and Delinke is 336 cm. How tall is Lili?
Fill in the P(X-x) values to give a legitimate probability distribution for the discrete random variable X, whose possible values are -5 ,3 , 4, 5 , and 6.
Let f and g be defined in R and suppose that there exists M > 0 such that |f(x) − f(p)| ≤ M|g(x) − g(p)|, for all x. Prove that if g is continuous in p, then f will also be continuous in p.
Write the equation of the line that is parallel to y= 4x-7 and has a y- intercept at (0,5)
Calculate the area of the parallelogram with adjacent vertices (1,4, −2), (−3,1,6) 𝑦 (1, −2,3)
Consider mixing 150 ml, 0.1M, HCI with 100 ml, 0.2M, KOH solution. Determine the pH of final solution.
A salesperson earns a base salary of $600 per month plus a commission of 10% of the sales she makes. You discover that on average, it takes you an hour and a half to make $100 worth of sales. How many hours will you have to work on average each month for your income to be $2000?
Oi👋🏻 Toque em "Criar Nova Tarefa" para enviar seu problema de matemática. Um dos nossos especialistas começará a trabalhar nisso imediatamente!
If the mean of the following numbers is 17, find the c value. Produce an algebraic solution. Guess and check is unacceptable. 12, 18, 21, c, 13
It costs a manufacturer $2,500 to purchase the tools to manufacture a certain homemade item. If the cost for materials and labor is 60¢ per item produced, and if the manufacturer can sell each item for 90¢, find how many items must he produce and sell to make a profit of $2000?
6(k-7) -2=5
A rectangular swimming pool has a length of 14 feet, a width of 26 feet and a depth of 5 feet. Round answers to the nearest hundredth as needed. (a) How many cubic feet of water can the pool hold? cubic feet (b) The manufacturer suggests filling the pool to 95% capacity. How many cubic feet of water is this? cubic feet
f(r) = 1/r+9 find f(x^2) + 1
Find the number of liters of water needed to reduce 9 liters of lotion. shave containing 50% alcohol to a lotion containing 30% alcohol.