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Homework Statement
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?
Homework Equations
[itex]P(A) = \frac{N(A)}{N}[/itex]
[itex]A[/itex]  no more than one passenger enters any car
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.
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