Question

A four-person committee is chosen from a group of eight boys and six girls. If students are chosen at random, what is the probability that the committee consists of all boys?

Answer 1

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Answer 2

The probability that the committee consists of all boys is:

`(10)/(143)`

Explanation:

Since a committee of four people is to be formed from a group of:

8 boys and 6 girls.

This implies total number of people= 14.

Probability that the committee consist of all boys is calculated by taking the ratio of probability of selecting 4 boys from all boys and selecting 4 person from total number of person.

Hence, the probability is calculated by:

`\text{Probability}=(8_C_4)/(14_C_4)`

Now,

`8_C_4=(8!)/(4!* (8-4)!)\\\\\\8_C_4=(8!)/(4!* 4!)`

and

`{14}_C_4=(14!)/(4!* (14-4)!)\\\\\\14_C_4=(14!)/(4!* 10!)`

Hence, the probability is given by:

`\text{Probability}=(10)/(143)`

Hence, the probability is:

`(10)/(143)`