SOLUTION: An elevator has 4 passengers and 8 floors. Find the probability that no 2 passengers get off on the same floor considering that it is equally likely that a person will get off at a

Algebra ->  Probability-and-statistics -> SOLUTION: An elevator has 4 passengers and 8 floors. Find the probability that no 2 passengers get off on the same floor considering that it is equally likely that a person will get off at a      Log On


   

Question 381234: An elevator has 4 passengers and 8 floors. Find the probability that no 2 passengers get off on the same floor considering that it is equally likely that a person will get off at any floor.
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
8 floors, 4 passengers. I will assume that the passengers begin at the first floor all going up, and any passenger gets off BEGINNING at the 2nd floor only (no one gets off at the 1st floor!) We have to find the number of all ordered listings of four numbers out of seven, e.g., 2<3<7<8, 3<6<7<8, 4<5<6<8, etc. That can be done in 7C4 ways. The total numbers of ways 4 passengers can get off at 7 floors (starting at the 2nd!) is 7%5E4. Therefore the probability is 7C4%2F7%5E4+=+5%2F7%5E3+=+5%2F343.