0606 P22 - Mar 2021 - Q8 - 9 marks
7935
A photographer takes 12 different photographs. There are 3 of sunsets, 4 of oceans, and 5 of mountains.
(a) The photographs are arranged in a line on a wall.
(i) How many possible arrangements are there if there are no restrictions?
(ii) How many possible arrangements are there if the first photograph is of a sunset and the last photograph is of an ocean?
(iii) How many possible arrangements are there if all the photographs of mountains are next to each other?
(b) Three of the photographs are to be selected for a competition.
(i) Find the number of different possible selections if no photograph of a sunset is chosen.
(ii) Find the number of different possible selections if one photograph of each type, sunset, ocean and mountain, is chosen.
