Question

Jacqueline is picking out some movies to rent, and she is primarily interested in children's movies and dramas. She has narrowed down her selections to 15 children's movies and 9 dramas. How many different combinations of 3 movies can she rent if she wants at least two dramas?

Answer 1

Answer: Jacqueline can rent from 624 different combinations of 3 movies, given that she wants at least two dramas.

Step-by-step explanation: To find the number of different combinations of 3 movies Jacqueline can rent, given that she wants at least two dramas, we can break this into two cases:

She rents exactly two dramas and one children's movie.

She rents all three dramas.

For the first case:

Number of ways to choose 2 dramas out of 9 dramas = 9/2

Number of ways to choose 1 children's movie out of 15 children's movies = 15/1. So, the total number of combinations for the first case is ( 9/2 ) x ( 15/1 )

For the second case:

Number of ways to choose 3 dramas out of 9 dramas = 9/3

Now, the total number of combinations is the sum of the two cases:

Total combinations = 9/2 x 15/1 + 9/3

Let's Calculate: 9/2 =
`(9!)/( 2!(9-2)!) = 36`

15/1 =15

9/3 =
`(9!)/(3!9-3)!) = 84`

So, 36 x 15+ 84

540 + 84

624

So, Jacqueline can rent from 624 different combinations of 3 movies, given that she wants at least two dramas.

I hoped this cleared your confusion.