Question

A newspaper vendor sells three papers to 135 customers, the papers are the daily times, the observer and the new Nigeria. 70 customers buy the daily time, 60 the observer, 50 the new Nigeria, 17 buy both the daily times and the observer, 15 buy both the observer and the new time Nigeria, 16 the daily times and new Nigeria, how many customers brought (1) all the three papers​

Answer 1

3 customers brought all the three papers.

Explanation:

Let, D, O and N represents the three newspapers.

D = The daily times

O = The observer

N = The new Nigeria.

According to the given information,

`n(D\cup O\cup N)=135, n(D)=70,n(O)=60,n(N)=50`

`n(D\cap O)=17, n(O\cap N)=15, n(D\cap N)=16`

We know that,

`n(A\cup B\cup C) = n(A) + n(B) + n(C)-n(A\cap B)-n(B\cap C)-n(C\cap A) + n(A\cap B\cap C)`

Using this formula, we get

`n(D\cup O\cup N) = n(D)+n(O) + n(N)-n(D\cap O)-n(O\cap N)-n(N\cap D) + n(D\cap O\cap N)`

`135 =70+60+50-17-15-16 +n(D\cap O\cap N)`

`135 =132+n(D\cap O\cap N)`

`135 -132=n(D\cap O\cap N)`

`3=n(D\cap O\cap N)`

Therefore, 3 customers brought all the three papers.