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Question
There are 15 persons in a party and if each 2 of them shakes hands with each other, how many handshakes happen in the party?
Solution
Total number of person in the party = 15
Given if each 2 of the 15 persons shakes bands with each other.
∴ The total number of handshakes is same as the number of ways of selecting 2 persons among 15 persons.
This can be done in 15C2 ways.
Number of handshakes = 15C2
= `(15!)/(2!(15 - 2)!)`
= `(15!)/(2! xx 3!)`
= `(15 xx 14 xx 13!)/(2 xx 1 xx 13!)`
= 15 × 7
= 105
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