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Need help with number of equiprobable outcomes

  1. Oct 5, 2013 #1
    1. The problem statement, all variables and given/known data

    A subway train made up of [itex]n[/itex] cars is boarded by [itex]r[/itex] passengers [itex](r < n)[/itex],
    each entering a car completely at random. What is the probability of the
    passengers all ending up in different cars?

    2. Relevant equations

    [itex]P(A) = \frac{N(A)}{N}[/itex]

    [itex]A[/itex] - no more than one passenger enters any car

    3. The attempt at a solution

    Part 1. Finding the total number of equiprobable outcomes [itex]N[/itex]
    The book says that the number of equiprobable outcomes [itex]N[/itex] is [itex]n^r[/itex].
    I've set up a table (included in the attachment) with 3 cars and 2
    passengers and came up with only 6 equiprobable outcomes. What
    I don't understand is that the passenger will not be in two cars at
    once so why would the solution be [itex]N = n*n*...*n = n^r[/itex].

    EDIT:
    Another book with the same problem with the same solution.
     

    Attached Files:

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    Last edited: Oct 5, 2013
  2. jcsd
  3. Oct 5, 2013 #2

    Dick

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    Science Advisor
    Homework Helper

    The 6 you have there is the number of restricted outcomes where there aren't two passengers in any car N(A). The N in the problem is the number of total outcomes, where any number of passengers can be in a car. The N is 3^2=9. which is the n^r. The probablity is the quotient. Got it? The N isn't the restricted outcomes. N(A) is the restricted outcomes.
     
    Last edited: Oct 5, 2013
  4. Oct 5, 2013 #3
    Oh yeah. That's very stupid of me. :redface: Thanks Dick.
     

    Attached Files:

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