# Permutations and Combinations

If you need all the necessary details about permutations and combinations, you get the formulas, differences, examples and more, everything under one roof!

When it comes to business mathematics, permutations and combinations are two of the most important concepts to understand. In this blog post, we will discuss the basics of the two, including how to calculate them and the differences between the two. We’ll also provide some examples so you can see how these concepts work in practice. So let’s get started!

## What are Permutations and Combinations?

Permutations and combinations are two of the most basic concepts in business mathematics. But what, exactly, are they?

Permutations are a specific type of combination where order matters. For example, if you have five people in a room and want to know how many different ways you can seat them, that would be permutations. The order of the people in the room matters. If you have five people in a room and want to know how many different ways you can seat them, but don’t care about the order, that would be combinations.

Combinations are a specific type of permutation where order doesn’t matter. For example, if you have five people in a room and want to know how many different ways you can seat them, but don’t care about the order, that would be combinations.

## Differences Between Permutations and Combinations

There are differences between permutations and combinations:

Permutations and combinations differ in the sense that permutations require order while combinations do not. Permutations are concerned with all possible arrangements of a set of objects in a specific order. Combinations are concerned with all possible arrangements or groupings of items, but the order does not matter.

For example, if you have a group of five people and want to know how many different ways you can seat them at a table, you have a permutation.

If you want to know how many ways a team of five can be chosen from eight people, the answer is a combination.

## Types of Permutations

There are two types of permutation, the first being called “order permutations” and the second being called “combination permutations”.

### Order Permutations

These are when you have a specific order that you need to list the items in, such as when you are listing out all the different ways you can order a deck of cards.

### Combination Permutations

These are when you have a list of items that can be combined together in any order they choose – examples include all possible combinations of letters or numbers that you might use for a password.

## Types of Combinations

There are three types of combinations: permutations, combinations with replacement, and combinations without replacement.

### Permutations

This type of combination is when every item in the set can be chosen independently. For example, if you have a deck of cards and want to choose two cards, there are 52 possible permutations. It is not necessary for the cards to be unique, but you cannot choose the same card twice from a deck of 52 cards.

### Combinations with Replacement

This type of combination is when the items in a set can be chosen more than once, such as in a lottery.

Combinations without Replacement

This type of combination is when the items in a set cannot be chosen more than once, such as in a race.

## Permutations and Combinations Formulas

People usually have questions on permutations and combinations formulas. We have jotted down the permutations and combinations formulas with you for better understanding!

### Permutation Formula

The permutations formula is n!/(n-k)!.

Here, n is the number of items and k is the number of items being chosen at a time.

For example, if you have five items and want to choose three at a time, you would use the formula:

n!/(n-k)! = (n*(n-l)*(n-k))/((n-l)!*k!).

This comes out to be 120 permutations (or, P(n, k) = n!/(n-k)! ).

### Combinations Formula

The combination formula is n!/k!(n-k)!

n denotes the number of items, k is the number of chosen at a time and is the combination.

For instance, if you have five items and want to choose three at a time, you would use the formula:

n!/k!(n-k)! = (n*(n-l))/((k!*(n-l)!).

This gives us the result of 20 combinations.

You can also use permutations and combinations formulas in excel too.

### Conclusion

Students who want to learn the basics of business maths should read this post. It will help them understand how permutations and combinations can be used in their future careers. In addition, it is a good review for those looking to brush up on some forgotten skills that they learned years ago but don’t use often anymore. Let’s look at an example from our own lives- when we order coffee! How many ways are there to order coffee? There are literally limitless possibilities since you could have cream or sugar with your drink as well as different sizes, flavours, etc., which means there would be one million possible orders if someone was going through all of them systematically by ordering each combination separately (you’d probably run out of time before