Question

In a un ceremony, 25 diplomats were introduced to each other. suppose that the diplomats shook hands with each other exactly once. how many handshakes took place?

Answer 1

The question is asking 'how many different ways can we pair two diplomats to shake hand'?

The combination formula is given by: $\frac{n!}{(n-r)!r!}$

We have n = 25 and r = 2

Substituting into the formula we have

$\frac{25!}{(25-2)!2!} =300$ handshakes