Question

Each of t he 59 members in a high school class is required to sign up for a minimum of one and a maximum of three academic clubs. The three clubs to choose from are the poetry club, the history club, and the writing club. A total of 22 students sign up for the poetry club, 27 students for the history club, and 28 students for the writing club. If 6 students sign up for exactly two clubs, how many students sign up for all three clubs?

a. 20
b. 12
c. 18
d. 6

Answer 1

Explanation:

Given there are Total of 59 members

22 students signup for Poetry club

27 students signup for history club

28 students signup for writing club

6 students signup for exactly two clubs

i.e. n(1)+n(2)+n(3)=6

if x i.e. n(4) is the no of students who signup for all three clubs then

`n(total)=n(Poetry)+n(history)+n(writing)-\left ( n(1)+n(2)+n(3)\right )-2x`

59=22+27+28-6-2x

x=6

thus 6 students signup for three clubs