Question

Among a group of 20 students, 13 are members of the math club, 11 are members of the drama club, and 9 are members of both. how many of the 20 students are NOT members of either club

Answer 1

The number of students that are NOT members of either club is 5

Step-by-step explanation

Given:

Total number of students = n(U) = 20

Members of Math club = n(M) = 13

Members of Drama club = n(D) = 11

Members of both clubs = n(D n M) = 9

Desired Outcome

Number of students that are NOT members of either club.

Using Venn Diagram

Determine the numbers of student in Drama club ONLY

n(D only) = n(D) - n(D n M) = 11 - 9 = 2

Determine the numbers of student in Math club ONLY

n(M only) = n(M) - n(D n M) = 13 - 9 = 4

Determine the number of students that are NOT members of either club.

n(D u M)' = n(U) - n(D u M)

n(D u M)' = 20 - (2 + 9 + 4) = 20 - 15 = 5

Hence, the number of students that are NOT members of either club is 5