Question

In a get together of 78 colleague each colleague it at least one of the three food item named Idli Dhokla and dosa. Exactly 34 people ate idli 52 people ate dhokla and 39 people ate dosa. If 17 people ate all three items, then find the number of people who exactly ate 2 items ​

Answer 1

Answer:

30 people ate 2 items....

Hope you find this answer helpful....

Answer 2

The correct answer is 64.

Given: People having at least one of the food item (AUBUC) = 78.

People eating only idli  = 34.

People eating only dhokla  = 52.

People eating only dosa  = 39.

People who eat all the three items = 17.

To Find: People who eat exactly two items.

Solution:

Let the people who eat idli are = n(A) = 34

Let the people who eat dhokla are = n(B) = 52

Let the people who eat dosa are = n(C) = 39

n(A U B U C) = n(A) + n(B) + n(B) - n(A∩B) - n(B∩C) - n(C∩A) + n(A∩B∩C)

Here, n(A∩B), n(B∩C) and n(C∩A) represents people eating exactly two items.

78 = 34 + 52 + 39 - n(A∩B) - n(B∩C) - n(C∩A) + 17

78 = 142 - n(A∩B) - n(B∩C) - n(C∩A)

n(A∩B) + n(B∩C) + n(C∩A) = 64

Hence, the number of people who only eat exactly two items is 64.

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