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

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

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

5 boys:

5 boys from a set of 6. So

`C_(6,5) = (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​.