Question

In a class of 50 students, each one come to school by bus or buy bicycle or by foot. 25 by bus, 20 by bicycle and 30 on foot and 10 by all the three. Now how many students come to school exactly by 2 modes of transport.

Answer 1

Answer: There are 35 students who come to school exactly by 2 modes of transport.

Explanation:

Since we have given that

Number of students who come to school by bus=25

(denoted by 'A')

Number of students who come to school by bicycle = 20

(denoted by 'B')

Number of students who come to school on foot = 30

(denoted by 'C')

Total number of students=50

Since we know the formula for set is given by

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

$50=25+20+30-n(A\cap B)-n(B\cap C)-n(C\cap A)+10\\\\50=85-n(A\cap B)-n(B\cap C)-n(C\cap A)\\\\-35=-(n(A\cap B)+n(B\cap C)+n(C\cap A)\\\\35=(n(A\cap B)+n(B\cap C)+n(C\cap A)$

Hence, there are 35 students who come to school exactly by 2 modes of transport.