Permutations and combinations

Learning objectives

Distinguish arrangements, where order matters, from selections, where it does not, and calculate them with n!, ⁿPᵣ and ⁿCᵣ

Find the number of ways of arranging objects in a line when some are identical, such as the letters of a word with repeated letters, by dividing by the factorials of the repeats

Find the number of ways of arranging objects under restrictions, treating items that must be together as a single block, placing items that must be separated in the gaps between the others, and fixing items at the ends

Find the number of ways of selecting objects from several groups, including conditions such as at least one of a type or not both of two named people, by adding separate cases or subtracting from the total

Solve arrangement problems involving two or more rows of seats or positions