There are $12$ persons in a party, and if each two of them shake hands with each other, then how many hand shakes happen in the party?

66

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72

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108

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132

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Solution

The correct option is A $66$
The total number of hand shakes are same as the number of ways of selecting $2$ persons among $12$ persons
i.e. $^{12} C_{2} = \frac{12!}{2! 10!} = 66$

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Division and Distribution into Groups of Equal Sizes

Standard XII Mathematics

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There are 12 persons in a party, and if each two of them shake hands with each other, then how many hand shakes happen in the party?

The correct option is A 66The total number of hand shakes are same as the number of ways of selecting 2 persons among 12 persons i.e. 12C2=12!2!10!=66

There are $12$ persons in a party, and if each two of them shake hands with each other, then how many hand shakes happen in the party?

The correct option is A $66$
The total number of hand shakes are same as the number of ways of selecting $2$ persons among $12$ persons
i.e. $^{12} C_{2} = \frac{12!}{2! 10!} = 66$