Question

11. A basketball team of 16 players consists of 6 guards, 7 forwards, and 3 centers. The coach decides to randomly select 5 players to start the game. What is the probability of 2 guards,

2 forwards, and 1 center starting the game?

Answer 1

0.2163

Explanation:

Firstly, we need to evaluate the total number of possible outcomes. Since there are 16 players, and we are selecting just 5, the total number of possibilities is 16C5= 4,368

Now, we know we need 2 guards from 6 , 2 forwards from 7 and 1 center from 3 to start the game. Since we are selecting, it is a combination problem. These can be done in the following number of ways:

6C2 * 7C2* 3C1

The probability is thus (6C2 * 7C2* 3C1 )/16C5 = 945/4368 = 0.2163