I have the following problem:
Determine the probability that out of 5 people sitting on a bench, 3 of them are sitting next to each other.
I know this is a simple problem, but I'm unsure my logic is correct.
I first calculate the ways those 3 people are sitting next to each other - $3!$ and then I consider this as a one person so there are 3 ways this group of 3 people sit anywhere on the bench among the other 2. I divide by the total number of ways.
Is this correct?
Thanks in advance!