We have been given that there are total 8 floors and 7 people get on the elevator on the first floor.
Therefore, the total number of possible outcomes are [tex]7^7[/tex]
Now, on the second floor any person can get off. So there are total 7 possibilities for second floor.
Now, since 1 person is already get off in the second floor, so on the third floor there are 7 possibilities.
Similarly, for
fourth - 5 possibilities
fifth - 4 possibilities
sixth- 3 possibilities
seventh - 2 possibilities
eight - 1 possibility
Therefore, the required probability is given by
[tex]P(E)=\frac{n(E)}{n(S)} \\ \\ P(E)= \frac{7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1}{7^7} \\ \\ P(E)=\frac{5040}{823543} \\ \\ P(E)=0.00612[/tex]
Therefore, the probability is 0.00612
