Question

To make a committee 4 men are chosen out of 6 candidates. What is the probability that 2 certain people will serve on that committee

Answer 1

`(2)/(5)`

Explanation:

6 groups, and 4 certain people

6

C

4

`(6!)/((6-2)!(2!))`

1 × 2 × 3 × 4 × 5 × 6/1 × 2 × 3 × 4 × 1 × 2

1 × 2 × 3 × 4 × 5 × 6/1 × 2 × 3 × 4 × 1 × 2

5 × 6/ 1 × 2

30/2 = 15

15 possible combinations

4 people, and 2 specific ones

4

C

2

`(4!)/((4-2)!(2!))`

1 × 2 × 3 × 4/1 × 2 × 1 × 2

1 × 2 × 3 × 4/1 × 2 × 1 × 2

12/2 = 6

`(6)/(15)=((6)/(3) )/((15)/(3) ) =(2)/(5)`

Answer 2

The probability that 2 certain people will serve on that committee is 11.11%.

Explanation:

Since to make a committee 4 men are chosen out of 6 candidates, to determine what is the probability that 2 certain people will serve on that committee the following calculation must be performed:

4/6 = 2/3

1/3 x 1/3 = X

0.333 x 0.333 = X

0.1111 = X

Therefore, the probability that 2 certain people will serve on that committee is 11.11%.