3.1: Photograph arrangements and competition selections
A photographer takes 12 different photographs. There are 3 of sunsets, 4 of oceans, and 5 of mountains.
(a)(i)[1]
The photographs are arranged in a line on a wall.
How many possible arrangements are there if there are no restrictions?
(a)(ii)[2]
How many possible arrangements are there if the first photograph is of a sunset and the last photograph is of an ocean?
(a)(iii)[2]
How many possible arrangements are there if all the photographs of mountains are next to each other?
(b)(i)[2]
Three of the photographs are to be selected for a competition.
Find the number of different possible selections if no photograph of a sunset is chosen.
(b)(ii)[2]
Find the number of different possible selections if one photograph of each type (sunset, ocean, mountain) is chosen.