Question

8. In a shop. 380 people buy socks, 150 people buy shoes and 200 people buy belt.
If there are total 580 people who bought either socks or shoes or belt and only 30
people bought all the three things?so how many bought exactly two things​

Answer 1

Answer:

90

step by step explanation:

Let S, H and B represent the set of number of people bought socks, shoes and belt respectively.

So, n(S) = 380, n (H) = 150, n (B) = 200

n (S∪H∪B) =580, n (S∩H∩B) =30

Therefore, n (S ∪ H ∪ B ) = n ( S ) + n ( H )+ n ( B ) – n (S ∩ H ) – n (H ∩ B ) – n (B ∩ S ) + n ( S ∩ H ∩ B ),

Now, we will put values given in the formula,

580 = 380 + 150 + 200 - n (S ∩ H) – n (H ∩ B) – n (B ∩ S) + 30

This gives that,

n (S ∩ H) + n (H ∩ B) + n (B ∩ S) =180

But this includes the number of people who bought all the three items also. So we have to deduct these numbers of people from it.

Let, n (S ∩ H ∩ B) = a

As we can see from the Venn diagram,

n (S ∩ H)-a + n (H ∩ B)-a + n (B ∩ S)-a=the required number

n (S ∩ H) + n (H ∩ B) + n (B ∩ S)-3a

180 – 90 = 90

Hence, 90 people are there who bought exactly two things.

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