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5 persons entered a lift cabin in the cellar of a 7-floor building apart from cellar. If each of them independently and with equal probability can leave the cabin at any floor out of the 7 floors beginning with the first, then the probability of all the 5 persons leaving the cabin at different floors is

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$\frac{360}{2401}$

$\frac{5}{54}$

$\frac{51}{71}$

$\frac{5}{18}$

answer is A.

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