Explain every complement and the meaning of neighbouring ride seats

Three families comprising six adults and three children go on an outing to a theme park and travel together for the day.

(i) There are 15 amusement rides. A child insists on trying at least 2 of them. Calculate the number of ways this can be done.2 marks

(ii) On the Mummy Surprise rollercoaster, a passenger car has seats in 3 rows and 3 columns as shown.

(a) Calculate the number of ways the families can be seated without restrictions.1 mark

(b) Tom, the youngest child, insists on sitting next to his mother. Calculate the number of ways this can be done.2 marks

(iii) At lunch they are allocated a circular table with 9 seats. Calculate the seating arrangements if none of the children sit together.2 marks