Probability Involving Combinations of Classroom Seating

AI Thread Summary
The discussion focuses on calculating probabilities related to the random reseating of 28 students in a classroom. It seeks to determine the likelihood of exactly one student returning to their original seat and the probability of at least one student being reseated correctly. To find these probabilities, the total number of ways to scramble the students is considered, along with the methods to fix one student while scrambling the others. The probability of at least one student in their original seat is derived from the complement of the probability that no students are reseated correctly. The conversation emphasizes the mathematical approach to solving these probability questions.
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I am attempting to determine two probabilities in a scenario in which a classroom of 28 students with assigned seating is scrambled randomly and blindly reseated by the teacher. What is the probability that exactly one student is reseated in his or her original seat, and what is the probability that at least one student is reseated in his or her original seat. Thanks for the assistance!
 
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First of all, how many ways are there to scramble 28 things?

How many ways are there to fix 1 and scramble the other 27?

The probability that at least one student is reseated in his or her original seat is one minus the probability that no student is reseated in his or her original seat.
 

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