Six persons enter a lift on the ground floor of a nine floor apartment. Assuming that each of them independently and with equal probability can leave the lift at any floor beginning with the first, what is the probability that all the six persons are leaving the lift at different floors?

• ANS:- 8p6/8^6
  beside ground floor there are 8 floors. since a person can leave the cabin at any of the 8 floors..
  therefore there are 8 ways for a person to leave the cabin.
  so, total no. of ways in which 6 persons can leave the cabin= 8*8*8*8*8*8=8^6
  i.e total no of elementary events=8^6
  now total no. of ways in which 6 persons can leave lift cabin at
  different floors= no. of arrangements of 8 by taking 6 at a time=8p6
  thus favourable no. of elementary events=8p6
  hence,required probability=8p6/8^6
• 10 years agoHelpfull: Yes(5) No(0)
• TOTAl NO. OF WAYS=8^6
  PROBABIITY THAT 6 PERSONS WIll EXIT lIFT AT DIFFERENT FlOORS IS 8P6/8^6.
• 10 years agoHelpfull: Yes(1) No(0)