# Understanding Permutations

• 1MileCrash
In summary, In statistics class, permutations are frequently used to arrange elements in different ways. For a set of 13 elements, there are 13! ways to arrange them. If 2 elements are picked from the set, there are 13!/11! different results. However, the number of unordered pairs is 13!/(2!*11!).

#### 1MileCrash

In my statistics class I am making use of permutations very often. I need to make sure I understand this.

If I have a set of 13 elements, I can arrange that 13! different ways, because Psub(13,13) = 13!/0!.

If I pick 2 elements from those 13 elements, I can get 13!/11! different results.

Is that what it means?

It depends whether you care about the order of the two picked. If it's an unordered pair, bear in mind that you could have picked the same two in either order.
Imagine the 13 elements in a row, and suppose the leftmost two will be the two picked. There are 13! orderings altogether. For a given pick of two, there are 2!*11! orderings that lead to it. So the number of such pairs is 13!/(2!*11!).

## 1. What is a permutation?

A permutation is an arrangement of objects in a specific order. It is a way of rearranging a set of objects where the order matters.

## 2. How many ways can a set of objects be permuted?

The number of possible permutations for a set of n objects is given by n factorial (n!). This means that for a set of 3 objects, there are 3 x 2 x 1 = 6 possible permutations.

## 3. What is the difference between a permutation and a combination?

A permutation takes into account the order of the objects, while a combination does not. For example, the permutations of the letters A, B, and C are ABC, ACB, BAC, BCA, CAB, and CBA. However, the combinations would only be ABC, ACB, and BAC, as the order does not matter in combinations.

## 4. How can permutations be used in real life?

Permutations are used in various fields such as mathematics, computer science, and statistics. In real life, they can be used to calculate the number of possible outcomes in a game, the number of possible combinations of a lock, or the number of possible arrangements of a certain number of people in a line.

## 5. Can the same set of objects have multiple permutations?

Yes, the same set of objects can have multiple permutations as long as the order of the objects is different. For example, the permutations of the letters A, B, and C are different from the permutations of the letters A, A, and B, as the order of the objects is different in each case.