10 people are randomly seated at a long bench Your probabili

10 people are randomly seated at a long bench. Your probability professor and his wife were among these 10 people. What is the probability that he and his wife sit next to each other?

Solution

There are 10! ways to arrange the people.

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To fix them together, imagine the couple as one body. Thus, there are just 9! ways to sit everyone. However, the couple can be permuted in 2! times.

Thus, the number of ways to do this is 9!2! ways.

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Thus, the probability of this is

P = [9!2!]/10! = 0.2 [ANSWER]