You select at random k numbers from the sequence 1, ...,n. Show that the probability that you will choose a particular combination of numbers, say, 1,2, ...,k, is 1/ (n k). Suppose that now you select k numbers one at a time without replacement, and distinguish samples containing the same numbers but selected at different orders. That is, you consider ordered samples. Give an heuristic argument that the probability that the ordered sample you selected contains 1,2, ...,k (perhaps, in a different order) is the same 1/ (n k). Prove it rigorously.