Question

10. There are 12 men on the basketball team. 2 are centers, 5 are guards, the rest a forwards. What is the probability, as a percent, that out of two players chosen at random they would be a guard and a forward?

Answer 1

There are 12 men on the basketball team.

2 centers , 5 guards , 5 forward.

2 players are selected randomly.

We have to find probability that they would be a guard and a forward.

Total number of ways to select 2 players from 12 = 12C2 = 66   

{ Using combination formula ,    nCr = n! / r!(n-r)! }

Number of ways to select 1 guard from 5 = 5C1 = 5

Number of ways to select 1 forward from 5 = 5C1 = 5

Total number of ways to select a guard and a forward in two players = 5*5 = 25

Probability = Number of favorable outcome / Total outcomes.

Probability that they would be a guard and a forward is ,

= 25/66 = 0.3789 = 37.88%

The probability that out of two players chosen at random they would be a guard and a forward is 37.88%