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Permutations and Combinations |
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Permutations and combinations |

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Permutation • Combination • Pascal's triangle |

In algebra, **permutations and combinations** are what I like to call the "Mathematical Barber Shop." Why? Because math problems get **perm**utations and **comb**inations!

Yes, that is off the topic, but it'll help in the long run.

Anyway, let's get on to what makes up this mathematical barber shop.

## PermutationsEdit

*Full article: Permutation*

Permutations are arrangements of items in a particular order, e.g., of any three items ABC, AB is a different arrangement than BA.

This is how permutations are denoted: *n*P*r*, where it is a **P**ermutation of *n* items arranged by *r* items at a time. Therefore, *r* ≤ *n*.

If *r* = *n* in *n*P*r*, then *n*P*r* = *n*!.

Here's how *n*P*r* is formulated:

$ nPr = \frac{n!}{(n-r)!}\, $

## CombinationsEdit

*Full article: Combination*

Combinations are arrangements of items with no regards to order, e.g., of any three items ABC, AB is the same arrangement as BA.

This is how combinations are denoted: *n*C*r*, where it is a **C**ombination of *n* items arranged by *r* items at a time. Therefore, *r* ≤ *n*.

If *r* = *n* in *n*C*r*, then *n*C*r* = 1.

Here's how *n*C*r* is formulated:

$ nCr = \frac{n!}{r!(n-r)!}\, $

...or...

$ nCr = \frac{nPr}{r!}\, $