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If there are 12 persons in a party, and ...

If there are 12 persons in a party, and if each two of them shake hands with each other, how many handshakes happen in the party?

A

66

B

132

C

12

D

11

Text Solution

Verified by Experts

The correct Answer is:
A
The total number of handshakes is the same as the number of ways of selecting 2 persons among 12 persons, i.e., `\ ^{12} C_{2}`.
`Rightarrow\ ^{12} C_{2}=frac{12 !}{10 ! times 2 !}=66`
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