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(a) There are six runners in a race, numbered 1, 2, 3, 4, 5, and 6. You observe

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Question

(a) There are six runners in a race, numbered 1, 2, 3, 4, 5, and 6. You observe that runner 6 finishes before runner 5, but do not know anything else about the order in which the runners finish. How many possible orders of finishing are there for the six runners? (b) In addition to observing runner 6 finish before runner 5, suppose that someone tells you that runner 2 finished before runner 1, and runner 1 finished before runner 3. How many possible orders of finishing are there given this new information?

Explanation / Answer

(a) There are six runners in a race, numbered 1, 2, 3, 4, 5, and 6. You observe

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