SOLUTION: There are 6 men and 4 women in club. A team of 4 members has to be chosen. Find the number of different ways of selecting the team if: a) All the members are to be of the same

Algebra ->  Permutations -> SOLUTION: There are 6 men and 4 women in club. A team of 4 members has to be chosen. Find the number of different ways of selecting the team if: a) All the members are to be of the same       Log On


   

Question 1150272: There are 6 men and 4 women in club. A team of 4 members has to be
chosen. Find the number of different ways of selecting the team if:
a) All the members are to be of the same sex.
b) There must be an equal number of men and women. Given that the 4 women include 2 sisters, find the total number of ways in which the team can be selected if either of the sisters, but not both, must be included.
Answer by VFBundy(438) About Me  (Show Source):
You can put this solution on YOUR website!
a) All the members are to be of the same sex.

Ways to choose 4 men: 6C4 = 6%21%2F%284%21%2A2%21%29 = 15
Ways to choose 4 women: 4C4 = 4%21%2F%284%21%2A0%21%29 = 1

Ways to choose all members of the same sex: 15 + 1 = 16

b) There must be an equal number of men and women. (Without sister provision.)

Ways to choose 2 men and 2 women: 6C2 * 4C2 = %286%21%2F%282%21%2A4%21%29%29%2A%284%21%2F%282%21%2A2%21%29%29 = 15 * 6 = 90

Given that the 4 women include 2 sisters, find the total number of ways in which the team can be selected if either of the sisters, but not both, must be included.

Let's re-categorize the people as such:

6 men
2 non-sisters
1 sister (A)
1 sister (B)

Ways to choose 2 men, 1 non-sister, and sister (A): = 15 * 2 * 1 = 30
Ways to choose 2 men, 1 non-sister, and sister (B): = 15 * 2 * 1 = 30

Ways that the team can choose 2 men and 2 women, where one of the women must be a "sister," but the other woman cannot be a "sister":

30 + 30 = 60