(CIE/0606/2021/m/22Q8)
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?$[1]$
(ii) How many possible arrangements are there if the first photograph is of a sunset and the last photograph is of an ocean? $\quad[2]$
(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. $\quad[2]$
(ii) Find the number of different possible selections if one photograph of each type (sunset, ocean, mountain) is chosen.
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