To solve this problem, we can consider each person as a distinct entity and calculate the number of ways they can leave the lift one by one.

First person:
The first person can choose any of the 8 floors to exit the lift. Hence, there are 8 possibilities for the first person.

Second person:
The second person can also choose any of the remaining 7 floors to exit the lift. Since the first person has already chosen one floor, there are 7 remaining possibilities for the second person.

Third person:
Similarly, the third person has 6 remaining floors to choose from, as two floors have already been selected by the first and second person.

Fourth person:
The fourth person has 5 remaining floors to choose from, as three floors have already been selected by the first, second, and third person.

Fifth person:
Finally, the fifth person has 4 remaining floors to choose from, as four floors have already been selected by the previous four people.

To find the total number of ways they can leave the lift, we need to multiply the number of possibilities for each person:

Total number of ways = 8 * 7 * 6 * 5 * 4 = 6720

However, the question asks for the number of ways, not the total number of ways. This means that the order in which the people leave the lift does not matter. Hence, we need to divide the total number of ways by the number of ways the 5 people can be arranged, which is given by 5P5.

5P5 = 5!/(5-5)! = 5!/0! = 5!

Therefore, the number of ways the 5 persons can leave the lift is:

Total number of ways = 6720/5! = 6720/120 = 56

Hence, the correct answer is option C) 7P5.

A is correct answer .