In how many ways can six students be seated in a row of 6 desks?
Suppose the students are A, B, C, D, E, and F
a) if two of the six students insist on sitting
next to each other
Suppose the students who insist on sitting next
to each other are A and B.
Then there are two cases of arranging 5 "things"
in a row.
Case 1: The 5 "things are AB, C, D, E, and F
That's 5!
Case 2: 5 "things are BA, C, D, E, and F
That's also 5!
Answer 5! + 5! = 120 + 120 = 240 ways.
b) if two of the six students refuse to sit next
to each other
First we find the number of ways they can sit
without restrictions:
That's 6! = 720
Then we subtract the 240 ways from the first
part of the problem:
720 - 240 = 480 ways.
Edwin