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Question

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


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Solution

A number of handshakes happen at the party.

The combination is the number of ways of selecting objects such that the order of selection is not to be counted.

Combination Formula:

nCr=nr=nPrr!=n!r!(nr)!

The total number of handshakes is the same as the number of ways of selecting 2 persons among 12 persons i.e.,

Numberofhanshake=12C2=12×112[nCr=n!r!(nr)!=n(n1)(n2)(nr+1)r!]=66

Hence, 66 handshakes happen at the party.


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