Question

In a group of 20 people who like rock, country, and classical music, 14 like rock, 17 like classical, 11 like both rock and country, 9 like both rock and classical, 12 like both country and classical, and 8 like rock, country, and classical.

How many like country music?_________________

Answer 1

Answer: There are 13 people who like country music.

Explanation:

Since we have given that

Number of people who like rock n(A) = 14

Number of people who like classical n(B) = 17

Let the number of people who like country n(C) be 'x'.

Number of people who like both rock and country = 11

Number of people who like both rock and classical = 9

Number of people who like both country and classical = 12

Number of people who like rock, country and classical = 8

As we know the formula:

n(A∪B∪C)=n(A)+n(B)+n(C)-n(A∩B)-n(B∩C)-n(C∩A)+n(A∩B∩C)

`20=14+17+x-11-9-12+8\\\\20=31+x-32+8\\\\20=x+7\\\\20-7=x\\\\x=13`

Hence, there are 13 people who like country music.