Permutation

Additional Mathematics

Multiplication rule

if an event can occur in m ways and a second event can occur in n ways, then both events can occur in m × n ways

The number of permutations of n objects

n!, where n! = nPn = n × (n – 1) × (n – 2) × … × 3 × 2 × 1

Permutation of n objects in a circle

The number of permutations of n objects taking r each time

The number of permutations for n different objects taking r objects each time and arranged in a circle

A permutation of an object in a circle where clockwise and anticlockwise arrangements are the same

the number of ways is

The number of permutations for n objects involving identical objects

where a, b and c, … are the number of identical objects for each type

Multiplication rule

can also be applied to more than two events

Permutation

The number of ways to arrange objects

Addition rule

A method used to determine the number of ways for events which are not sequential and are mutually exclusive