In a building there are 12 floors plus the ground floor. 9 people get into the lift of the building on the ground floor. The lift does not stop on the first floor. If 2,3 4 people get out of the lift on its upward journey,in how many ways can they do so? (Assume the passengers get out on different floors).

1) 11C3 * 3P3
2) 11P3 * 9C4 * 5C3
3) 10P3 * 9C4 * 5C3
4) 12C3

• Total Number of Floors = 12 + 1 (ground floor) = 13
  No. of stops = 13 - 1 - 1 = 11
  ( since,
  Lift doesn't stop at Floor 1
  All passengers get into lift at ground floor)
  
  Total no. of stops required = 3
  ( Since, Passengers will get out in groups of 2,3 & 4)
  
  No. of ways to select 3 stops = 11P3
  
  No. of passengers in lift = 9
  
  out of 9 passengers 4 will get out at once. So, we have to choose any 4 from 9 passengers and that can be done in 9C4 ways.
  
  Now remaining passengers = 9 - 4 = 5
  
  out of 5 remaining passengers 3 will get out at once. So, we have to choose any 3 from 5 passengers and that can be done in 5C3 ways.
  
  Now remaining passengers = 5 - 3 = 2
  
  All the remaining passengers will get out at once. So, that can be done in 2C2 ways = 1
  
  Therefore,
  
  Total no. of ways = 11P3 * 9C4 * 5C3
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