Question

You and your friends pick up seven movies to watch over a holiday. You have time to watch only two. In how many ways can you select the two to watch?

Answer 1

There are 21 ways to select the two movies to watch.

Explanation:

In mathematics, the procedure to select k items from n distinct items, without replacement, is known as combinations.

The formula to compute the combinations of k items from n is given by the formula:

`{n\choose k}=(n!)/(k!(n-k)!)`

It is provided that there are n = 7 movies to watch.

But we only have time for k = 2.

Compute the total number of ways in which we can select 2 movies from 7 as follows:

`{7\choose 2}=(7!)/(2!(7-2)!)`

`=(7!)/(2!* 5!)\\\\=(7* 6* 5!)/(2!* 5!)\\\\=(7*6)/(2* 1)\\\\=21`

Thus, there are 21 ways to select the two movies to watch.