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At a swim competition, swimmers compete in heats (races) against each other for a variety of different events. Suppose a pool has 8 lanes, each

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At a swim competition, swimmers compete in "heats" (races) against each other for a variety of different events. Suppose a pool has 8 lanes, each one containing a swimmer for a given race. The top three finishers in the race are awarded 1st, 2nd, and 3rd place and recognized for their accomplishment with a trophy. How many different ways can the top three finishers be awarded out of the 8 swimmers

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