SOLUTION: Five people check identical suitcases before boarding an airplane. At the baggage claim, each person takes one of the five suitcases at random. What is the probability that exactly
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-> SOLUTION: Five people check identical suitcases before boarding an airplane. At the baggage claim, each person takes one of the five suitcases at random. What is the probability that exactly
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Question 1210187: Five people check identical suitcases before boarding an airplane. At the baggage claim, each person takes one of the five suitcases at random. What is the probability that exactly one person ends up with the wrong suitcase?
You can put this solution on YOUR website! Let's break down this problem step by step.
**1. Total Possible Outcomes**
* There are 5 people and 5 suitcases.
* The total number of ways the suitcases can be distributed is 5! (5 factorial) = 5 * 4 * 3 * 2 * 1 = 120.
**2. Favorable Outcomes (Exactly One Person Wrong)**
* It is impossible for exactly one person to get the wrong suitcase. Here's why:
* If one person gets the wrong suitcase, that means another person *must* get the suitcase that belongs to the first person.
* Therefore, at least two people must get the wrong suitcases.
**3. Probability**
* Since there are no ways for exactly one person to get the wrong suitcase, the number of favorable outcomes is 0.
* Probability = (Favorable Outcomes) / (Total Possible Outcomes)
* Probability = 0 / 120 = 0
**Therefore, the probability that exactly one person ends up with the wrong suitcase is 0.**
The probability is clearly 0, by logical reasoning.
If exactly one person ends up with the wrong suitcase, then the other four people each end up with the right suitcases. But that means the fifth person would also have the right suitcase.
