[Solved] If there are 12 persons in a party and if each of them shake (2024)

Concept:

The combination formula is used to find the number of ways of selecting items from a collection, such that the order of selection does not matter. In simple words, combination involves the selection of objects or things out of a larger group where order doesn’t matter.

\(\Rightarrow _{}^{n}\textrm{C}_{r}= \frac{n!}{(n-r)!\times r!}\)

Calculation:

The total number of handshakes is the same as the number of ways of selecting 2 persons among 12 persons, i.e.,\(_{}^{12}\textrm{C}\)₂.

\(\Rightarrow _{}^{12}\textrm{C}_{2}= \frac{12!}{10!\times 2!}=66\)

Hence, If there are 12 persons at a party and each of them shakes hands with each other, then the number of handshakes in the party is 66.