Separate labelled circular seats from fixed-room colour assignments

(a) Five couples are to be seated at a round table with numbered seats. Find the number of ways such that each wife must sit next to her husband.3 marks

(b) Mr Lin wants to repaint his four bedrooms. Each room can only be painted with one colour. From six different colours, find the number of ways the four rooms can be painted if

(i) there is no restriction on the colours used,1 mark

(ii) there is no repetition of colours used,1 mark

(iii) he chooses exactly two colours.3 marks