Suppose Mr and Mrs Smith along with 8 other individuals will

Suppose Mr. and Mrs. Smith along with 8 other individuals will be randomly seated in 10 chairs that are arranged in a row in a concert hall. Find the probability that Mr. and Mrs Smith will end up seating next to each other.

Solution

There are 10! ways to permute all 10.

If we want the couple to sit together, we treat them as 1 body (but can be permuted in 2! ways). Thus, the other 8 has 8! ways to permute.

Thus, we have 2!8! ways to do the job.

Thus,

P = (2!8!)/10! = 0.022222222 [answer]