6persons enter a lift on the ground floor of a 9floor apartment. Assuming that each of them independently & with equal probability can leave the lift at any floor beginning with the first, what is the probability that all the 6persons are leaving the lift at different floors? Pick:
A) 7P6/8^6 B) 5P6/8^6 C) 8P6/8^6 D) 9P6/8^2 E) 8P6/8^3
Apart from the ground floor, there are 8 floors   Let's find out the total number of ways in which all the six persons can leave the   lift at eight different floors   The 1st person can leave the lift in any of the 8 floors (8 ways)   The 2nd person can leave the lift in any of the remaining 7 floors (7 ways)   The 3nd person can leave the lift in any of the remaining 6 floors (6 ways)   ...   The 6th person can leave the lift in any of the remaining 3 floors (3 ways)   Total number of ways = 8 × 7 × 6 × 5 × 4 × 3 = 8P6   (In fact, from the definition of permutations itself,   we will be able to directly say that the number of ways in which all the six persons   can leave the lift at 8 different floors = 8P6)   n(E)= Total Number of ways in which all the six persons can leave the lift at eight   different floors = 8P6   Now we will find out the total number of ways in which each of the six persons   can leave the lift at any of the eight floors   The 1st person can leave the lift in any of the 8 floors (8 ways)   The 2nd person can leave the lift in any of the 8 floors (8 ways)   The 3nd person can leave the lift in any of the 8 floors (8 ways)   ...   The 6th person can leave the lift in any of the 8 floors (8 ways)   Total number of ways = 8 × 8 × 8 × 8 × 8 × 8 = 86   i.e., The total number of ways in which each the six persons can leave the lift   at any of the eight floors = n(S) = 86   P(E) = n(E)n(S)=8P6/8^6   8P6/8^6
<result>C</result>
6persons enter a lift on the ground floor of a 9floor apartment. Assuming that each of them independently & with equal probability can leave the lift at any floor beginning with the first, what is the probability that all the 6persons are leaving the lift at different floors?