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If there are $12$ persons in a party, and if each of them shakes hands with each other, then number of handshakes happen in the party is

A

66

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B

48

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C

72

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D

None of these

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Solution

The correct option is A 66
Total number of handshakes
$=$ The number of ways of selecting $2$ persons from among $12$ persons
$=^{12} C_{2} = \frac{12 \times 11}{2 \times 1} = 66$

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