Permutations and combinations

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

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.

Permutations

 * 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 Pr, where it is a Permutation of n items arranged by r items at a time. Therefore, r ≤ n.

If r = n in nPr, then nPr = n!.

Here's how nPr is formulated:

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

Combinations

 * 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 Cr, where it is a Combination of n items arranged by r items at a time. Therefore, r ≤ n.

If r = n in nCr, then nCr = 1.

Here's how nCr is formulated:

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

...or...

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