Question

Tanisha is picking out some movies to rent, and she is primarily interested in mysteries and foreign films. She has narrowed down her selections to 17 mysteries and 8 foreign films. How many different combinations of 4 movies can she rent?

Answer 1

Tanisha can make 12,650 different combinations of 4 movies from her selection of 17 mysteries and 8 foreign films. This is calculated using the combinations formula C(n, k) = n! / (k!(n-k)!).

Step-by-step explanation:

Tanisha is looking at different combinations of movies she can rent. To find out how many different combinations of 4 movies she can pick from 17 mysteries and 8 foreign films, we can treat the problem as a combination problem in mathematics. The total number of films she is considering is 17 + 8 = 25.

Using the formula for combinations, which is C(n, k) = n! / (k!(n-k)!), where n is the total number of items to choose from, k is the number of items to choose, and ! represents the factorial of a number, we calculate the number of ways to select 4 movies from 25.

The calculation would look like C(25, 4) = 25! / (4!(25-4)!). This simplifies to C(25, 4) = (25 × 24 × 23 × 22) / (4 × 3 × 2 × 1) = 12,650 different combinations of 4 movies she can rent.