Question

In a group of students, 30 played chess, 19 played volleyball, 25 played
basketball, 14 played both volleyball and chess, 8 played both baskethall
and volleyball, 15 played both basketball and chess and 5 played both
three events. How many played chess only, basketball only and volleyball
only? How many students are there in all?

Answer 1

Answer:

Explained below.

Step-by-step explanation:

Denote the events as follows:

C = chess

V = volleyball

B = basketball

The data provided is as follows:

n (C) = 30

n (V) = 19

n (B) = 25

n (C ∩ V) = 14

n (B ∩ V) = 8

n (B ∩ C) = 15

n (C ∩ V ∩ B) = 5

Consider the Venn diagram below.

The number of students who played only chess is marked in pink:

n (Only C) = 6

The number of students who played only volleyball is marked in blue:

n (Only V) = 2

The number of students who played only basketball is marked in orange:

n (Only B) = 7

The number of students who played all three is marked in grey:

n (C ∩ V ∩ B) = 5