# A chess club has 10 members, of whom 6 are men and 4 are women

#### zx0xc0

A chess club has 10 members, of whom 6 are men and 4 are women. A team of 4 members is selected to play in a match. Find the number of different ways of selecting the team if

Given that the 6 men include 2 brothers, find the total numberof ways in which the team can be selected if either ofthe brothers, but not both, must be included.

#### 123qwerty

Let's split the club into two parts: the brothers and everyone else. Then the total number of ways in which the team can be selection is $$\displaystyle 2 \times \displaystyle{8 \choose 3}$$.