Five persons entered the lift cabin on the ground floor of an 8-floor building. If each of them can leave the cabin independently at any floor beginning with the first; find the total number of ways in which each of the five persons can leave the cabin: (i) at any one of the 7 floors and (ii) at different floors.

Answer

(a)`7^(5)` (b) 2520

Explanation

Let `A_(1),A_(2),A_(3),A_(4),A_(5)` are five persons.
(a) `A_(1)` can leave the cabin at any of the seven floors. So, `A_(1)` can leave the cabin in 7 ways. Similarly, each of `A_(2),A_(3),A_(4),A_(5)` can leave the cabin in 7 ways. Thus, the total number of ways in which each of the five persons can leave the cabin at any of the seven floors is `7xx7xx7xx7xx7=7^(5)`
(b)` A_(1)` can leave the cabin at any of the seven floors. So, `A_(1)` can leave the cabin in 7 ways. Now, `A_(2)` can leave the cabin at any of the remaining 6 floors. So, `A_(2)` can leave the cabin in 6 ways. Similarly, `A_(3),A_(4) " and" A_(5)` can leave the cabin in 5, 4 and 3 ways respectively. Thus, the total number of ways in which each of the five persons can leave the cabin at different floors is `7xx6xx5xx4xx3=2520`