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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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