Question

Among 75 players 50 like basketball, 15 like both basketball and volleyball. If each player likes at least one of the games, then what is the number of players who like only volleyball?

• A. 15
• B. 10
• C. 20
• D. 25

Answer 1

The correct option is D 25



If A = set of players liking basketball
B = set of players liking volleyball
then $n\left(A\right)=50$
$n(A\cap B)=15n(A\cup B)=75$
As,$n(A\cup B)=n\left(A\right)+n\left(B\right)-n(A\cap B)75=50+n\left(B\right)-15n\left(B\right)=40$
Number of people who like volleyball only $=n\left(B\right)-n(A\cap B)=40-15=25$