My Name Is (Was)...
Suppose a magician has N people write their full names on a 3 x 5 card and toss them into a hat. Later, the magician asks each to draw a card blindly--one card per person. Assume that no two people share the same name and that there is a uniform probability that any particular card can be drawn by any particular person. What is the probability that none of the people will end up with their own card?
Hint: Get a group of people together an simulate it as an experiment. The larger the size of the group, the better.
Solution Commentary: The answer approaches 1/e for very large n, but your experiment should produce a reasonable approximation for 1/e.
If you want to explore this problem further, it is commonly known as the Hat Check Problem. do a search on the internet or look at this "understandable" proof by Richard Scoville in The American Mathematical Monthly (Vol. 73#3, March 1966, pp. 262-265).