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

Answer:

There are 75 ways to form the committee.

Step-by-step 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.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

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:

$T = C_{6,2}C_{5,4} = \frac{6!}{2!4!} \times \frac{5!}{1!4!} = 3*5*5 = 75$

There are 75 ways to form the committee.