20 professors are having a tea party, 6 physicists and 14 mathematicians. To prepare, they need to choose: 3 people to set the table, 2 people to boil the water, and 6 people to make the scones. Each person can only do 1 task. (Note that this doesn’t add up to 20. The rest of the people don’t help.) (a) In how many different ways can they choose which people perform these tasks? (b) Suppose that the physicists all hate tea. If they only give tea to 10 of the 20 people, what is the probability that they only give tea to mathematicians?

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