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There are 7 different people who can stand in the first place. For each of those people, there are 6 people who could stand in the second place, as one person is already placed. For each of these combinations there are 5 people who could take the third place, and so on. This means that the total number of arrangements (assuming the people are all standing in a line) is 7! = 7x6x5x4x3x2x1 = 5040
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Mathematically speaking, if you line them up in one straight line, there are 5040 ways. You do 7*6*5*4*3*2*1=5040. The * means multiply.
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