> ## Documentation Index
> Fetch the complete documentation index at: https://math.aboneda.com/llms.txt
> Use this file to discover all available pages before exploring further.

# Counting

## Overview

* Counting as an idea
* Combinatorics and the Factorial
* Combination vs Permutation

## nPr vs nCr

| Feature        | nPr (Permutation)                                                    | nCr (Combination)                                                   |
| -------------- | -------------------------------------------------------------------- | ------------------------------------------------------------------- |
| **Meaning**    | Arrangements of items where **order matters**                        | Selection of items where **order does not matter**                  |
| **Formula**    | $P(n, r) = \frac{n!}{(n - r)!}$                                      | $C(n, r) = \frac{n!}{r!(n - r)!}$                                   |
| **Common Use** | Creating passwords, seating charts, or race rankings (1st, 2nd, 3rd) | Choosing a committee, drafting a team, or selecting lottery numbers |
| **Relation**   | $P(n, r) = C(n, r) \times r!$                                        | $C(n, r) = \frac{P(n, r)}{r!}$                                      |