1. * (Logic). Eight pawns are placed on eight random squares on a chess board. What is the probability that no two pawns are in the same row or the same column?
2. Which is more likely:
(a) obtaining at least one six in six rolls of a fair die or
(b) obtaining at least one double six in six rolls of a pair of fair dice?
Remark. This question was posed to Isaac Newton and has some history associated with it.
2. * (Coincidence). Suppose each of n sticks are broken into two pieces, one longer than the other. Then the 2n pieces are paired up to make n new sticks. Find the probabilities that the pieces are all paired up in their original order and that each long piece is paired up with some short piece. (There are two events in this problem.)