Question

A committee that consists of five members are to be chosen from 6 boys and 5 girls. Find the number of different committees that can be formed if the number of boys is more than the number of girls​

Answer 1

Answer:

281 different committees can be formed if the number of boys is more than the number of girls​.

Step-by-step explanation:

The order in which the people are chosen to the committee 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.

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

Number of boys more than the number of girls:

3, 4 or 5 boys.

3 boys:

3 boys from a set of 6.

2 girls from a set of 5. So

$C_{6,3}C_{5,2} = \frac{6!}{3!3!} \times \frac{5!}{2!3!} = 200$

4 boys:

4 boys from a set of 6.

1 girl from a set of 5. So

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

5 boys:

5 boys from a set of 6. So

$C_{6,5} = \frac{6!}{5!1!} = 6$

Total:

200 + 75 + 6 = 281

281 different committees can be formed if the number of boys is more than the number of girls​.