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

Apr 2016
2
0
DUBAI
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.
 
Dec 2012
850
310
Hong Kong
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 \(\displaystyle 2 \times \displaystyle{8 \choose 3}\).