Five person entered the lift cabin on the ground floor of an $8$ floor house. Suppose of that each of them independently and with equal probability can leave a cabin at any floor beginning with the first, then the probability of all $5$ persons leaving at different floors is:

16807

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16907

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2520

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2580

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Solution

The correct option is C $2520$
Suppose there are five persons.
The first person can leave the lift cabin in $7$ different ways.
The second person can leave the lift cabin in $6$ different ways.
The third person can leave the lift cabin in $5$ different ways.
The fourth person can leave the lift cabin in $4$ different ways.
The fifth person can leave the lift cabin in $3$ different ways.
Thus, by product rule,the total number of ways, in which each of the five persons can leave the lift cabin at different floors $= 7 \times 6 \times 5 \times 4 \times 3 = 2520$

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Five person entered the lift cabin on the ground floor of an 8 floor house. Suppose of that each of them independently and with equal probability can leave a cabin at any floor beginning with the first, then the probability of all 5 persons leaving at different floors is:

Five person entered the lift cabin on the ground floor of an $8$ floor house. Suppose of that each of them independently and with equal probability can leave a cabin at any floor beginning with the first, then the probability of all $5$ persons leaving at different floors is: