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Math Help - Probaility And Combination Question

  1. #1
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    Probaility And Combination Question

    Question:

    7 passengers enter an elevator on the first floor of an 11-floor building.
    Assume that the egress pattern to floors 2,3,....,11 is the same. What is the probability that all get off at different floors?

    My Answer:


    Number of objects to be arranged = 7passengers + (11floor - first floor - 1) = 16 objects
    Possible arrangements = 16C7 = ways of egress
    Ways of all get off at different floors = 9C2 ( 9 floors, 2 floors with no passenger gets out)

    P(probability that all get off at different floors) = 9C2/16C7 = 0.00315 <---------Which is WRONG!!!!!

    The correct answer is 0.0605, but I have no idea on how to do it, I am so frustrated ...
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  2. #2
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    Hello, csy0961743!

    7 passengers enter an elevator on the first floor of an 11-floor building.
    Assume that the egress pattern to floors 2,3, ... ,11 is the same.
    What is the probability that all get off at different floors?

    Each of the 7 people have 10 choices of floors on which to exit.

    . . There are: . 10^7 possible outcomes.


    How many ways can they exit on different floors?

    There are: . _{10}P_7 \:=\:\dfrac{10!}{3!} \:=\:604,\!800 ways.


    Answer: . \dfrac{604,\!800}{10,\!000,\!000} \;=\;0.06048
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