In a group of 65 people, 40 like cricket and 10 like both cricket and tennis.
How many like tennis only and not cricket? How many like tennis?
Given:
In a group of 65 people:
- 40 people like cricket
- 10 like both cricket and tennis
To Find:
- Number of people like tennis only
- Number of people like tennis
Let us consider,
Number of people who like cricket $=n(C)=40$
Number of people who like tennis $=n(T)$
Number of people who like cricket or tennis $=n(C \cup T)=65$
Number of people who like cricket and tennis both $=n(C \cap T)=10$
Venn diagram:
Now,
$n(C \cup T)=n(C)+n(T)-n(C \cap T)$
$65=40+n(T)-10$
$n(T)=65-40+10$
$=35$
Therefore, number of people who like tennis = 35
Now
Number of people who like tennis only $=n(T-C)$
$n(T-C)=n(T)-n(C \cap T)$
$=35-10$
$=25$
Therefore, the number of people who like tennis only = 25