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-- The first place can be any one of 20 students. For each of these, -- the second place can be any one of the remaining 19 students. For each of these, -- the third place can be any one of the remaining 18 students. For each of these, -- the fourth place can be any one of the remaining 17 students. So the four places can be assigned in any one of (20 x 19 x 18 x 17) = 116,280 ways.

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