Something to get the gears in your brain going for the new year.
There are 50 people (excluding the band) at Rachel’s birthday ceilidh, 20 men and 30 women (as often seems to be the way of things). Ewan, the caller, has just announced that everyone should get ready for a bit of Gay Gordons, a dance that requires everyone to go into couples.
My question is, if everyone is up for this dance, how many different ways can everyone be split up into pairs?
You may assume that, due to the lack of men, the women will be content to pair up with each other and the men won’t (as usually happens).
(I should say you probably shouldn’t worry about attempting this if you don’t know what a factorial is.)