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k numbers are chosen at random from the set {1,2,...,N}, one after the other, without replacement....

k numbers are chosen at random from the set {1,2,...,N}, one after the other, without replacement. Find the probabilities of each of these events:

1. The set of numbers drawn is {1,2,...,k}. (Note that they need not be drawn in that exact order since we only care about the set.)

2. The numbers are chosen in an ascending order.

3. How do your answers to parts 1 and 2 change if the numbers are drawn one after the other, but with replacement? (Interpret ascending as strictly increasing. For example, if we draw the numbers 1, 2, 2, 3, then this would not be an ascending sequence.)

Math   Statistics-And-Probability   
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