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?

Question

asked Aug 24, 2020 114k views

1 Answer

Tomer Ariel · Answer 1 · 2020-08-28T04:42:50+0000

Answer: 42

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.