A) \[\frac{^{n}{{P}_{m}}}{{{m}^{n}}}\]
B) \[\frac{^{n}{{P}_{m}}}{{{n}^{m}}}\]
C) \[\frac{^{n}{{C}_{m}}}{{{m}^{n}}}\]
D) \[\frac{^{n}{{C}_{m}}}{{{m}^{n}}}\]
Correct Answer: B
Solution :
Since, a person can alight at any one of n floors. Therefore, the number of ways in which m passengers can alight at n floors is \[\underbrace{n\times n\times n\times .....\times n={{n}^{m}}.}_{m\,times}\] The number of ways in which all passengers can alight at different floors is \[^{n}{{C}_{m}}\times m!{{=}^{n}}{{p}_{m}}.\] Hence, required probability \[\frac{^{n}{{p}_{m}}}{{{n}^{m}}}.\]
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