# Permutation & Combination

Combination & Permutation deals with arrangement of thing. If the order doesn't matter, then it is called **Combination**. If the order does matter, then it is a **Permutation**.

In other words, **Permutation is an ordered Combination.**

### Permutation

^{n}P_{r} = n!/(n-r)!

There are basically two types of permutation:

- When repetition is allowed
- No repetition

**1. Permutations with Repetition**

To choose *r* things from n when repetition is allowed, the permutations are:

**n × n × ... (r times) = n ^{r}**

(Because there are **n** possibilities for the first choice, then there are **n** possibilities for the second choice, and so on.)

### Combinations

Number of ways objects can be selected from a group.

^{n}C_{r} = ^{n}P_{r} / r!

### Circular Permutations

**Circular Table**

A circular table has no fixed starting or ending point. If n persons are to be arranged in a straight line, there are n! unique ways. When n persons are to sit around a circular table, each arrangement will be repeated n times, There will be (n-1)! different arrangements.

**Circular Wire**

Arrangement of beads (which are all different) around a circular wire differs from table. Why? Because when you turn it over, you can see other side of it like a mirror image. So, total number of different arrangements decreases by half. Thus, n beads on a circular wire can be arranged in (n-1)!/2 ways.