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It’s the end of the morning break at Addwell School, and ten classrooms, packed with enthusiastic students, are waiting for their next lesson to begin.
Ten teachers leave the staffroom one by one after consuming their morning coffee. The first to leave is Professor Hamnee Shah, who can’t remember which class he is timetabled to teach, so he chooses a class at random and begins teaching them.
The second teacher does the following: goes to their timetabled classroom. If there is no teacher inside, they teach their scheduled class. Otherwise, they choose a random class with no teacher and begin teaching. Every one of the remaining eight teachers does the same. What is the probability that the last teacher out of the staffroom (Ms Lattelike) teaches their timetabled class?
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