Question

In how many ways can a family of six be seated at a round table if the mother and father must sit together?

Answer 1

treat the "mother and father" as one entity.
So we are arranging 5 around the table
which is 5!
but we can rotate each particular arrangement 5 times around the table without changing any order, since there is no specified position around the table
(e.g. everybody get up and move one seat to the right, the seating order is still the same. We can do this 5 times)

number of ways = 5!/5 = 4!
BUT, we could sit Mother-Father or Father-Mother, so
number of ways = 2x4! = 48

Answer 2

48