Question

5 women and 7 men are eligible to serve on a committee. If a committee of 4 is randomly selected, what is the probability that it will consist of 2 women and 2 men?

Answer 1

The required probability is
`(14)/(33)`.

Explanation:

Probability:

The ratio of the favorable outcomes to the all possible outcomes.

Given that, 5 women and 7 men are eligible to serve on a committee.

A committee of 4 is randomly selected.

Choosing 2 women out of 5 women is

`=^5C_2`

`=(5!)/(2!(5-2)!)`

`=(5!)/(2!3!)`

=10

Choosing 2 men out of 7 men is

`=^7C_2`

`=(7!)/(2!(7-2)!)`

`=(7!)/(2!5!)`

=21

Total number of eligible person is = (5+7)=12

Choosing 4 member out of 12 member is

=
`^(12)C_4`

`=(12!)/(4!(12-4)!)`

=495

The required probability is

`=(10* 21)/(495)`

`=(14)/(33)`