Question

110 freshmen participated in sports or clubs or both. 55 are involved in sports and 68 are involved in clubs. How many students are involved in just sports?

Answer 1

Answer: 42

Step-by-step explanation:

Let A represents the number of freshmen participated in sports and B represents the number of  freshmen participated in clubs.

Then , we have given that

$n(A)=55\\\\n(B)=68\\\\n(A\cup B)=110$

Using formula

$n(A\cup B)=n(A)+n(B)-n(A\cap B)$

We have,

$110=55+68-n(A\cap B)\\\\\Rightarrow\ n(A\cap B)=123-110=13$

Now, the number of students are involved in just sports is given by :-

$n(A)-n(A\cap B)=55-13=42$

Hence, 42 students are involved in just sports.