Question

In how many ways can a committee of 3 men and 4 boys be chosen from 7 men and 6 boys so as not to include the youngest boy if the eldest man is serving?

Answer 1

There are 75 ways to form the committee.

Explanation:

The order in which the people are chosen is not important, which means that the combinations formula is used to solve this question.

Combinations formula:

`C_(n,x)` is the number of different combinations of x objects from a set of n elements, given by the following formula.

`C_(n,x) = (n!)/(x!(n-x)!)`

In this question:

Considering the eldest has to be there, 2 men from a set of 6 and 4 boys from a set of 5(excluding the youngest), so:

`T = C_(6,2)C_(5,4) = (6!)/(2!4!) * (5!)/(1!4!) = 3*5*5 = 75`

There are 75 ways to form the committee.