Question

The manager of a four-screen movie theater is deciding which of 12 available movies to show. The screens are in rooms with different seating capacities. How many ways can he show four different movies on the screens?

Answer 1

The manager can show four different movies on the screens in 495 ways.

Step-by-step explanation:

The manager of the movie theater has 12 available movies to choose from. However, he only wants to show four different movies on the screens. To find the number of ways he can show four different movies, we can use the concept of combinations.

The formula for calculating the number of combinations is n choose k where n is the total number of movies and k is the number of movies to choose.

In this case, n = 12 (total number of movies) and k = 4 (number of movies to choose).

Using the formula, we can calculate the number of ways as:
C(12, 4) = 12! / (4! * (12-4)!)

Simplifying the expression:

C(12, 4) = (12 * 11 * 10 * 9) / (4 * 3 * 2 * 1)

C(12, 4) = 495

Therefore, there are 495 ways in which the manager can show four different movies on the screens.