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Three people all set down their identical notebooks on a table.
On the way out, they each randomly pick up one of the notebooks. What is the probability that none of the three people pick up the notebook that they started with?
That's correct probability!
What was the case?
Let's name peoples as Person - 1, Person - 2, Person - 3 and their notebooks as Notebook - 1, Notebook - 2 and Notebook 3 respectively.
Now there can be 6 ways 3 notebooks can be distributed among 3 persons like below.
(Here, for convenience, 3 different colors are assigned to the notebooks of 3 persons.)
As we can see, there are only 2 cases, where the each of person not getting own notebook. In rest of cases, at least 1 person got own notebook & notebooks of others are shuffled between 2.
So the probability that none of the three people pick up the notebook that they started with is 2/6 = 1/3.
