Five persons enter a lift cabin in the cellar of a $7$-floor building (excluding the 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 that all $5$ persons leave the cabin at different floors is:
- A$\frac{360}{2401}$
- B$\frac{5}{54}$
- C$\frac{51}{71}$
- D$\frac{5}{18}$
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