A television show was attended by 12 well known celebrities. Each one of them shook hands with each other once at the beginning of the show. Find the number of handshakes that took place on the show.

There are 12 celebrities. A handshake needs 2 people.
This simply means in how many ways 2 people can be selected out of 12.

So the answer is ¹²C₂

ⁿC_r = n!/r!(n - r)!

∴ ¹²C₂ = 12!/2!(12 - 2)! = (12 × 11)/2
= 66 = number of handshakes. [If there are n people and they shake hands only once with each other, then, Number of handshakes = ⁿc₂ = n(n -1)/2]