Some time ago, critic Ivor Smallbrain threw a lavish party for 5 of his best friends, including a private showing of the fabulous new Ally Wooden film Everything You Wanted to Know About Sets But Were Afraid to Ask. It was a rainy day, and each guest brought their own umbrella. At the end of the party, somewhat the worse for wear, Ivor handed each friend a random umbrella, and off they went into the night.

Work out the chance that nobody got their own umbrella.

Do the same calculation for the three subsequent parties thrown by Ivor, to which he invited 6,7 and 8 guests, respectively. Do you notice anything interesting?