Question

Each of the 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?

Answer 1

6 students

Explanation:

Total number of students = 59

Number of poetry = 22

Number of history = 27

Number of writing = 28

Number who signed for exactly 2 = 6

Number who singed up for all 3 = x

Using the knowledge of Venn diagram:

n(Total) = n(Poetry) + n(History) + n(Writing) - n(Exactly 2) - 2x

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

59 = 77 - 6 - 2x

59 = 71 - 2x

59 - 71 = - 2x

-12 = - 2x

x = 6