Question

How many different groups of 3 movies can a person rent if there are 12 movies to choose from?

Answer 1

If there are 12 movies and a person can rent three, then there are 220 different combinations they can be rented in.

Answer 2

The different groups of 3 movies can a person rent if there are 12 movies to choose from is:

220

Explanation:

We know that choosing of r items out of a total given n items is given by the method of combination and the formula for the doing so is given by:

`n_C_r=(n!)/(r!* (n-r)!)`

Here we have to chose 3 movies out of 12 movies.

Hence, we have n=12 and r=3

Hence, the number of ways of doing so is given by:

`{12}_C_3=(12!)/(3!* (12-3)!)\\\\\\{12}_C_3=(12!)/(3!* 9!)\\\\\\{12}_C_3=(12* 11* 10* 9!)/(3!* 9!)\\\\\\{12}_C_3=(12* 11* 10)/(3* 2)\\\\\\{12}_C_3=220`

Hence, the answer is:

220