Question

In the next Olympics, the United States can enter four athletes in the diving competition. How many different teams of four divers can be selected from a group of nine divers?

a. 36

b. 6,561

c. 126

d. 3,024

Answer 1

The correct option is C.

Explanation:

From the given information it is clear that the total number of divers in a group is 9.

The number of selected divers is 4.

The total ways to select r items from total n item is

`^nC_r=(n!)/(r!(n-r)!)`

Using this combination formula, the number of different teams of four divers that can be selected from a group of nine divers is

`^9C_4=(9!)/(4!(9-4)!)`

`^9C_4=(9!)/(4!5!)`

`^9C_4=(9* 8* 7* 6* 5!)/(4* 3* 2* 1* 5!)`

Cancel out common factors.

`^9C_4=126`

Therefore the correct option is C.