South African Mathematics Olympiad

The person on the extreme left can be any one of the four people that is neither Alfred nor Mollie; the second left can be any one of the remaining three; the first person on the right of centre... and so on. For every arrangement of the people around them, Alfred and Mollie can swap places to make a new arrangement. So the number of possibilities is $(4\times 3\times 2\times 1)\times 2=48$.