Lottery. A lottery specifies a random subset R of r out of the first n natural numbers by picking one at a time. Determine the probabilities of the following events: (a) there are no consecutive numbers, (b) there is exactly one pair of consecutive numbers, (c) the numbers are drawn in increasing order. Suppose that you have picked your own random set of r numbers. What is the probability that (d) your selection matches R?, (e) exactly k of your numbers match up with numbers in R?