Chapter 15.4, Problem 14P

(a) Find the probability that in two tosses of a coin, one is heads and one tails. That in six tosses of a die, all six of the faces show up. That in 12 tosses of a 12 -sided die, all 12 faces show up. That in $n$ tosses of an $n$-sided die, all $n$ faces show up.

(b) The last problem in part (a) is equivalent to finding the probability that, when $n$ balls are distributed at random into $n$ boxes, each box contains exactly one ball. Show that for large n, this is approximately $e^{-n}\sqrt{2\pi n}.$