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The answer is 7! = 5040 ways. Label the 7 people A through G. Person A can pick from 7 different available positions. Person B can now choose from 6 different positions. Person C can choose from 5 available positions. On down to person G has one choice, so this is 7 x 6 x 5 x 4 x 3 x 2 x 1 = 5040. This type of multiplication is so common in statistics that it has a name - factorial function, and is abbreviated by the exclamation mark (n! = n x (n-1) x (n-2) x ... x 2 x 1)

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