Permutations and combinations

Learning objectives

Distinguish a permutation, in which the order of selection matters, from a combination, in which it does not, and decide which applies to a given situation

Evaluate and use the notation n!, ⁿPr = n!/(n − r)! and ⁿCr = n!/(r!(n − r)!), including the conventions 0! = 1 and ⁿC₀ = 1

Count the number of arrangements of a set of different objects in a row, including arrangements subject to a restriction such as two particular objects being kept together or apart (problems with repeated identical objects or circular arrangements are not set)

Count selections made from one or more groups, for example choosing a committee with a fixed number of members from each of two categories, by multiplying the relevant combinations

Handle conditions such as at least or at most by adding the counts for separate cases or subtracting the unwanted cases from the total, and form numbers from given digits with no digit repeated