Counting Outcomes

Combination

A selection of a set of objects, regardless of the selection order.

Permutation

An arrangement of a set of objects, with regard to the order of the arrangement.

Rule 1

Suppose there is an experiment consisting of number of steps. And -th step having number of outcomes.

Rule 2

Total number of combinations of objects taken at a time is:

Rule 3

The number of permutations of objects taken at a time is:

Rule 4

The number of circular permutations of objects taken from a group of objects:

Rule 5

Suppose a multi-set contains items of different types. There are number of type objects. Total number of distinct permutations: