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

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) (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 = = 15
Ways to choose 4 women: 4C4 = = 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 = = 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
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