wydawg: Tom and John are to sit in a row of 6 seats with 4 other people. How many ways are there for the 6 people to sit if both Tom and John refuse to sit on an end seat?
I am not 100% sure but this is what I think.
If you sit Tom and John first there will be 4P2 possibilities (Just for Tom and John)
There are 4 people and 4 chairs left so that will mean 4P4 possibilities for the others (afer Tom and John are already seated)
so altogether I think that there are 4P2 x 4P4 = 12 X 4! = 12 x 24 = 288 permutations.
I am reasonably sure that is correct.