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In a room containing $28$ people, there are $18$ people who speak English, $15$ people who speak Hindi and $22$ people who speak Kannada. $9$ persons speak both English and Hindi, $11$ persons speak both Hindi and Kannada whereas $13$ persons speak both Kannada and English. How many speak all three languages?

  1. $9$
  2. $8$
  3. $7$
  4. $6$
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5 Answers

Best answer
23 votes
23 votes
Apply set formula of $A$ union $B$ union $C$
$28 = (18 + 15 + 22) - (9 + 11 + 13) + x$
$28 = 55 - 33 + x$
$x = 6$

Correct Answer: $D$
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2 votes

 In question given that,

n(EUHUK) =28 ,n(E∩H) =9 ,n(E∩K) =11 ,n(H∩K) =13 ,n(E)=18 ,n(H)=15 , n(K)=22

n(EUHUK) =  n(E) + n(H)+ n(K) - [ n(E∩H) + n(E∩K) + n(H∩K) ] + n(E∩H∩k)

28 = 18 +15 +22 -[9+11+13] + n(E∩H∩k)

n(E∩H∩k) = 6

Option (D)6 ,is correct.

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0 votes

Let A be the people who speaks English.
Let B be the people who speaks Hindi.
Let C be the people who speaks Kannada.
(A∪B∪C) = A + B + C - (A∩B) - (B∩C) - (C∩A) + (A∩B∩C)
28 = 18 + 15 + 22 - 9 - 11 - 13 + (A∩B∩C)
∴ (A∩B∩C) = 6

Answer:

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