Question

In a class of 50 students each one come to school by bus , bicycle or by foot. 25 by bus. 20 by bicycle.30 by on foot and 10 students by all three. now how many students come to school exactly by two modes of transport?​

Answer 1

5 students come to school exactly by two modes of transport.

Given :

Total number of students = 50

Number of students who come to school by bus = n(A)= 25

Number of students who come to school bicycle = n(B) = 20

Number of students who come to school on foot = n(C) = 30

Total number of students = n(A∪B∪C) = 50

Number of students who come to school by all three modes of transport - n(A∩B∩C) = 10

Using formula-

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

50 = 25 + 20 +30 - n(A∩B) - n(B∩C) - n(C∩A) + 10

50 = 85 - n(A∩B) - n(B∩C) - n(C∩A)

n(A∩B) - n(B∩C) - n(C∩A) = 85 - 50

n(A∩B) - n(B∩C) - n(C∩A) = 35

Finding the students who come exactly by two modes :-

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

= (A∩B + B∩C + C∩A ) - 3 *(A∩B∩C)

= 35 - 3(10)

= 35 - 30

= 5

Hence : Number of students who come to school by two modes of transport = 5