Permutations and Combinations – Notes

Fundamental Principle of Counting

If an event can occur in m different ways, following which another event can occur in n different ways, then the total number of the occurrence of the events in the given order is m  n.

Introduction to Permutation

A permutation is an arrangement in a definite order of a number of objects taken some or all at a time.

The number of permutations of n different objects taken r at a time is equal to ⁿP_r, where 0 < r  n. Permutations

The number of permutations of n distinct objects taken r at a time, where repetition of the objects is allowed, is n^r.