probability question

Question

The moderator of a forum discussion s assigning seats to the six participants. If the seats are arranged in linear fashion, determine the probability that Dr. Sarah and Dr. Mathew are seated next to each other.

Answer 1

Assuming order matters:

There are 6!/4! ways to sit two people among six = 30 ways

Assuming order matters here are the following 10 ways to sit Dr. S and Dr. M next to each other:

1 2 3 4 5 6

S M

M S

S M

M S

S M

M S

S M

M S

S M

M S

Thus the probability of Dr. M and Dr. S sitting next to each other is 10/30 = 1/3