In how many ways can a family of seven sit round a table if the mother and father must sit together?

Answer 1

Treat the Father-Mother as one person, so now you are seating only 6.
Let's put MF in one of the seats, so with caring about the actual place around the table there would be 6*5! ways to do that.
BUT, supposedly there are no distinct seats, so the number of ways is 6*5!/6 = 5!
(image everybody getting up and moving one seat to the left, no new arrangement is created, but we could do this 6 times, therefore I divided by 6)
BUT, we could have seated father and mother as FM or MF, so the
number of ways to arrange the family is 2*5!