Riddles, brain puzzles and mathematical problems

[Froge]

20 pianists participate in a competition. Out of these 20, 3 played Bach and 5 played Schumann. 6 out of the 20 pianists are chosen at the end of the competition to receive a prize.

What is the probability that, out of the prize winners, at least two played Bach or none played Schumann?

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/CStards

Suppose you have a set of n numbers, n >= 3. You are given an integer k. Write a program (in C or pseudocode) that calculates the total number of ways 3 numbers can be chosen from the set to add up to k. There may be duplicates in the set, but each number of the set is considered different. No need to do input, just write algorithm and return output.