set theory

Question

in a group of students  100 studying Hindi,100 studying Maths and 100 studying English,20 people studying Maths and Mnglish,40 studying English and Hindi,60 studying Hindi and Maths,210 students are studying  only 1 subject.How many are studying all three?

Comments

50 ??

Answer 1

is answer 70?

Answer 2

n(H) = 100

n(M) = 100

n(E) = 100

n(M ∩ E) = 20

n(E ∩ H) = 40

n(H ∩ M) = 60

n(H $\cup$ M $\cup$ E $\cup$) = 210

n(H $\cup$ M $\cup$ E $\cup$) = 100 + 100 + 100 - 20 - 40 - 60 + n(H ∩ M ∩ E)

Therefore, n(H ∩ M ∩ E) = 70