Question

A basketball team has 8 players. In how many different ways can the coach select 2 players to be the captains for tonight's game? A.16. B.28. C.56. D.64

Answer 1

Option: B is the correct answer.

B. 28

Explanation:

It is given that the total number of players in a basketball team are: 8

Now in order to select two players out of the total 8 players we need to use the method of combination since the objective is just to chose them and not to arrange.

Hence, the number of ways of doing so is calculated as:

`8_C_2`

which is solved as:

`8_C_2=(8!)/(2!* (8-2)!)\\\\\\8_C_2=(8!)/(2!* 6!)\\\\\\8_C_2=(8* 7* 6!)/(2* 6!)\\\\\\8_C_2=(8* 7)/(2)\\\\\\8_C_2=28`

Hence, the number of ways of doing so is:

28

Answer 2

Since the problem is not concerned about the order of choosing the captain, the concept used is the combination. From 8 players, 2 are to be chosen,
8C2
The numerical value of the combination is 28. Thus, the answer is letter B.