Probability Involving Combinations of Classroom Seating

[v_bledsoe]

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!

 

[mutton]

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.