In a meeting of 45 people, there are 40 people who know one another and the remaining know no one. People who know each other only hug, whereas those who do not know each other only shake hands. How many handshakes occur in this meeting?

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CSIR UGC (NET) Mathematical Science: Held On (7 June 2023)
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  1. 225
  2. 10
  3. 210
  4. 200

Answer (Detailed Solution Below)

Option 3 : 210
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Detailed Solution

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Explanation:

Total people in meeting is 45 and out of then 40 people know each other.

So 5 people don't know anyone.

Let those 5 peoples be A, B, C, D, E

So A will handshake 44 people.

B will handshake 43 people

will handshake 42 people

D will handshake 41 people

and E will handshake 40 people

Hence total handshake = 44 + 43 + 42 + 41 + 40 = 210

Option (3) is correct

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