Question

From a group of 6 girls and 7 boys, how many 5-member committees consist of: members of the same gender?

Answer 1

Answer:

27 5-member committees consist of members of the same gender

Step-by-step explanation:

The order in which the members are chosen to the group is not important, so we use the combinations formula 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.

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

All girls:

5 girls from a set of 6. So

$C_{6,5} = \frac{6!}{5!(6-5)!} = 6$

All boys:

5 boys from a set of 7. So

$C_{7,5} = \frac{7!}{5!(7-5)!} = 21$

Total:

Either all girls or all boys.

6 + 21 = 27

27 5-member committees consist of members of the same gender