In a school, a student can opt the language subject out of English, Hindi and Sanskrit either single or in a combination. 50 students opted English, 62 Hindi and 42 Sanskrit. If there are total 78 students and only 12 opted for all three languages, then the number of students who opted for exactly two languages is
Let E, H, S be the sets of students who opted for English, Hindi and Sanskrit respectively.
n(E)=50
n(H)=62
n(S)=42
n(E∪H∪S)=78
n(F∩B∩C)=12
We know, n(E∪H∪S)=n(E)+n(H)+n(S)−n(E∩H)−n(H∩S)−n(E∩S)+n(E∩H∩S)
78 = 50 + 62 + 42 −n(E∩H)−n(H∩S)−n(E∩S) + 12
⇒ n(E∩H) + n(H∩S) + n(E∩S) = 88
"The number of students who opted for exactly two languages = n(E∩H) + n(H∩S) + n(E∩S) − 3×n(E∩H∩S) = 88 − 3x12 = 52
The whole world is mathematics and mathematics is the whole world.
Rajat Rokade
The difference between a two-digit number and the number obtained by interchanging the digits is 36. What is the difference between the sum and the difference of the digits of the number if the ratio between the digits of the number is 1 : 2 ?