What is a Permutation?
A permutation is a mathematical technique that determines the number of possible arrangements in a set when the order of the arrangements matters. Common mathematical problems involve choosing only several items from a set of items with a certain order.Permutations are frequently confused with another mathematical technique called combinations. However, in combinations, the order of the chosen items does not influence the selection. In other words, the arrangements ab and be in permutations are considered different arrangements, while in combinations, these arrangements are equal.
Representation of Permutation
We can represent permutation in many ways, such as:
Permutations vs. Combinations
Both permutation and combinations involve a group of numbers. However, with permutations the order of the numbers matters. With combinations, the ordering does not matter. For example, with permutation, the order matters, such as the case with a locker combination.
Locker combos are, thus, not combinations. They are permutations. A locker combo must be entered exactly as scripted, such as 6-5-3, or it will not work. If it were a true combination then the numbers could be entered in any order and work.
There are various types of permutations as well. You can find the number of ways of writing a group of numbers. But you can also find permutations with repetition. That is, the total number of permutations when the numbers can be used more than once or not at all.
A Few Examples
Here’s a few examples of combinations (order doesn’t matter) from permutations (order matters).
- Combination: Picking a team of 3 people from a group of 10. C(10,3) = 10!/(7! · 3!) = 10 · 9 · 8 / (3 · 2 · 1) = 120.Permutation: Picking a President, VP and Waterboy from a group of 10. P(10,3) = 10!/7! = 10 · 9 · 8 = 720.
- Combination: Choosing 3 desserts from a menu of 10. C(10,3) = 120.Permutation: Listing your 3 favorite desserts, in order, from a menu of 10. P(10,3) = 720.
Don’t memorize the formulas, understand why they work. Combinations sound simpler than permutations, and they are. You have fewer combinations than permutations.