The question is asking 'how many different ways can we pair two diplomats to shake hand'?
The combination formula is given by: [tex] \frac{n!}{(n-r)!r!} [/tex]
We have n = 25 and r = 2
Substituting into the formula we have
[tex] \frac{25!}{(25-2)!2!} =300[/tex] handshakes
