In a class of 50 students, each one come to school by bus or by bicycle or on foot. 25 by bus, 20 by bicycle, 30 on foot and 10 students by all the three. Now how many students come to school exactly by two modes of transport?
Answers
Answer : 5 students.
5 students come to school exactly by two modes of transport.
Explanation :-
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
Answer=5 student
5 student come exactly by two modes of transport
Given
total no. of student=50
no. of student who come by bus=n(A) =25
no. of student who come by bus=n(B) =20
no. of student who come by foot=n(C) =30
no. of student who come by all three modes=n(Anbnc) =10
after using all formulas it is 85-50=35
find student who come by two modes
after using formula according it is
35-3(10)
35-30
5