How many time you have used the word permutation and combination wrong? Even though we use the term ‘combination’ to identify passwords – its usage in this sense is not accurate. The set of characters working as a password I permutation in essence not combination. So, what is the difference between them and how can we calculate them accurate? I am going all in this article, a permutation of a set is defined as the arrangement of set members into a linear order or sequence. In case the set is already in order, permutation is the rearrangement of the elements. The word permutation is translated into changing the ordered set. Permutation is different from combination as the selection of the members does not consider the order. Permutation is the ways of selecting ‘r’ elements out of total ‘n’ objects. It is the number of ways an object or element can be selected and the order of the number is important. Imagine you are dealing with a deck of nine card ranging from 1 to 9. After drawing 3 cards randomly, now you place these cards on the table – how many sequences can you make by the drawn cards?

## Permutation Formula

The formula for permutation is easier as compared to other mathematical and statistical formulas. The general permutation formula is expressed in the following way:

## Permutation – Formula

Where:

- n – The total number of elements in a set
- k – The number of selected elements arranged in a specific order
- ! – Factorial

Factorial (noted as “!”) is the product of all positive integers less than or equal to the number preceding the factorial sign. For example, 3! = 1 x 2 x 3 = 6.

The formula above is used in situations when we want to select only several elements from a set of elements and arrange the selected elements in a special order.

## Example of Permutation

Imagine you are a partner in an equity firm and you want to invest $6 million in two projects. Rather than going for the equal investment in two different projects, you invested $4 million in project A which is more promising to you. Now you have $2 million and you invested it in project B which seem less promising to you. Your market analyst came up with 6 different option for you to decide. How many arrangements are available to you in this case? This is a permutation problem. As the allocation of investment for both projects is unequal, the selection order matters in this case. For instance you can invest $4 million in project or you can also invest $2 million in project A. As the option in this case are not equal, it is important that you use the formula to assess the arrangement options available for you.

## Permutation and Combination Calculator

This is the same difference in permutation and combination calculator. In case of calculations, permutation calculator consider the sequence of the number. Combination calculator is mainly used for estimating the combination of different number. Permutation calculation on the other hand is used to identify the specific pattern of the set. The major difference between combination calculator and permutation calculator is their focus on number sequence and pattern.

## Permutation Vs Combination

There is huge difference between permutation and combination and that difference is the ordering sequence. In case of permutation, the sequence of the number or the order is focused while in case of combination the order is not the focus of attention. Let’s assume the combination of your locker is 5432. If you enter 4325 it won’t open because the ordering is different (permutation).

The permutations of 2, 3, 4, 5 are:

5432, 5423, 5324, 5342, 5234, 5243, 4532, 4523, 4325, 4352, 4253, 4235, 3542, 3524, 3425, 3452, 3254, 3245, 2543, 2534, 2435, 2453, 2354, 2345

The ‘combo’ of your locker is a specific number permutation of 2, 3, 4, & 5.

Your locker “combo” is a specific permutation of 2, 3, 4 and 5. If your locker worked truly by combination, you could enter any of the above permutations and it would open!

## nCr Calculator

Combination calculator can find the combination of elements with ease. The formula of combination is as follow:

For n ≥ r ≥ 0.

The formula indicates that there are multiple approaches through which you can obtain the value of ‘r’. The value will be extracted from “’n’ number of elements where order is not significant and repetition is not allowed. “The number of ways of picking r unordered outcomes from n possibilities.” Also referred to as r-combination or “n choose r” or the binomial coefficient. In some resources the notation uses k instead of r so you may see these referred to as k-combination or “n choose k.”

Combination is defines as an approach to select objet, item, or elements from a specific calculation where the order of selection is not significant. Let’s assume that a set contains three numbers A, B, and C. The ways you can select two numbers from the provided set will be known as combination.

If the data set is limited, you can count the number of combinations manually. In case where data set is large, the combination of set will also be higher causing difficulty in the manual calculation. Combination formula can be used in such cases to find the possibility of number of combination that can be attained,

Combination calculator works on the formula of combination to provide you accurate results every time. It can be used in cases where order or sequence of the element is not significant. Repetition is also not allowed to ascertain the accuracy of the obtained result.

A permutation calculator can help you calculate the sequence of the numbers in an ideal way. Rather than going through the hassle of manually calculating the order of any set, it is far better to just put the values in the calculator and get an accurate answer to the problem. Calculating the permutation and identifying the sequence and order of the set is easier than ever now. The chances of error through human error or manual calculations are far higher as compared to permutation calculator.