Question

Roxie is picking out some movies to rent, and she is primarily interested in horror films and foreign films. She has narrowed down her selections to 20 horror films and 8 foreign films.

Step 1 of 2 :  

How many different combinations of 3 movies can she rent?

Answer 1

There are total 20 + 8 = 28 films,

3 films are selected from 28 films by ²⁸C₃ ways,

²⁸C₃ = (28! / [ (28-3)! * 3! ]

= 28 ! / [ (25 ! * 3! ]

= 3276

Answer 2

To calculate the number of different combinations of 3 movies Roxie can rent, we can use the concept of combinations.

In mathematics, the number of combinations of selecting r objects from a set of n objects, without regard to the order, is given by the formula:

C(n, r) = n! / (r! * (n - r)!)

Where: C(n, r) represents the number of combinations of selecting r objects from a set of n objects. n! (n factorial) is the product of all positive integers from 1 to n. r! (r factorial) is the product of all positive integers from 1 to r. (n - r)! is the product of all positive integers from 1 to (n - r).

In Roxie's case: n = Total number of movies available = 20 (horror films) + 8 (foreign films) = 28 r = Number of movies she wants to rent = 3

Let's calculate the number of combinations:

C(28, 3) = 28! / (3! * (28 - 3)!) C(28, 3) = (28 * 27 * 26) / (3 * 2 * 1) C(28, 3) = 3276

So, Roxie can rent 3 movies in 3,276 different combinations from the available selection of horror films and foreign films.