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Twelve person...

Question

Twelve persons meet in a room and each shakes hand with all the others. Find the number of handshakes.

A

60

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B

66

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C

12

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D

24

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Solution

The correct option is B
66

First person shaking hands with second person and second person with first person will not be two different handshakes. Here, order is not important. There will be as many handshakes as there are combinations of 12 different things taken 2 at a time.

Total number of handshakes = $^{12} C_{2}$ = 66

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