1. Coloured Cube
How many distinct ways are there to colour the six faces of a cube using six different colours, and applying a different colour to each face. Cubes which could be rotated to look the same as each other are not counted as distinct.
2. Snap!
I have two identical packs of cards. I take each pack and shuffle it separately, placing them both face down in the table. I then procede to play a game of snap with myself - being a mathematician I have no friends. I compare the top card from each pile, and then compare the second card from each pile, ... and so on. What is the probability that I continue in this way all the way down the piles, and never find an exact match in the 52 pairs of cards?
3. A Birthday Shared...
Given 23 randomly selected people, what is the probablilty that at least two of them have their birthday on the same day of the year?
[ You may assume that none of them was born on 29th February, and that any other day of the year is equally likely to ocur as a birthday. ]