Question

A person at a library can choose books and movies to borrow. He decides to choose 4 movies and 6 books. How many combinations are possible?

Answer 1

490

Step-by-step explanation:

The number of ways or combinations to select x objects from a group of n is equal to

`\text{nCx}=(n!)/(x!(n-x)!)`

A person has 8 options for movies and he is going to select 4, the number of combinations for movies is

`8C4=(8!)/(4!(8-4)!)=70`

In the same way, the person has 7 options for books and he is going to select 6, so

`7C6=(7!)/(6!(7-6)!)=7`

Then, the total number of combinations for 4 movies and 6 books is calculated as:

70 x 7 = 490 possible combinations

Therefore, the answer is 490 possible combinations