Out of a group of 200 students (who know at least one language), 100 s

1.	Out of a group of 200 students (who know at least one language), 100 students know English, 80 students know Kannada, 70 students know Hindi. If 40 students know all the three languages, find the number of students who know exactly two languages.
Answer» writing n(E) = 100, n(K)= 80, n(H) = 70 . n(E ∪ K ∪ H) = 200, n (E ∩ K N ∩ H) = 40 We know that n(E ∪ K ∪ H) = n(E) + n (K) + n(H) –n (E ∩ K) – n (K ∩ H) -n (H ∩ E) + n (E ∩ K ∩ H) ∴ n (E ∩ K) + n (K ∩ H) + n (H ∩ E) = 90

Out of a group of 200 students (who know at least one language), 100 students know English, 80 students know Kannada, 70 students know Hindi. If 40 students know all the three languages, find the number of students who know exactly two languages.

Answer»

writing n(E) = 100, n(K)= 80, n(H) = 70 .

n(E ∪ K ∪ H) = 200, n (E ∩ K N ∩ H) = 40

We know that n(E ∪ K ∪ H) = n(E) + n (K) + n(H) –n (E ∩ K) – n (K ∩ H) -n (H ∩ E) + n (E ∩ K ∩ H)

∴ n (E ∩ K) + n (K ∩ H) + n (H ∩ E) = 90

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Out of a group of 200 students (who know at least one language), 100 students know English, 80 students know Kannada, 70 students know Hindi. If 40 students know all the three languages, find the number of students who know exactly two languages.

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