Permutation and Combination Calculator
With this permutation and combination calculator, we aim to help you to calculate the permutations and combinations of the given number of objects. This calculator will help you know what are the possible permutations and combinations.
We have written this article to help you understand the difference between the permutations and combinations and their respective definitions. We will also demonstrate some calculations examples to help you understand the permutation and combination formula. Moreover, our calculator also displays the possible permutations and combinations to help you understand the concept easier.
What is permutations and combinations?
Give the sample size, permutation is the number of ways that a certain number of objects can be arrange in a sequential order. On the other hand, combination is defined as the number of ways that a certain number of items can be groped together, given the sample size.
Both of these metrics is useful in calculating probabilities. Have you ever wonder what is your chances in winning a lottery? In order to win a lottery, you need to have the correct numbers in the right sequence. Hence, to answer this question you will need to understand permutation. Similar concept can also be applied to combination.
How to calculate permutations and combinations? Formula for combinations and permutations
To understand the calculation for permutations and combinations, let's look at some examples below.
For permutation, let's assume the following:
 Calculation: Permutation
 The total number of objects,
n
:6
 Sample size,
r
:3
You can calculate the number of possible permutation in three steps:
 Determine the total number of objects
This is the total number of objects that you possess. In this example,
n
is6
.
 Determine the sample size
This is the size of the permutations that you wish to compute. The
r
in this example is3
.
 Calculate the number of possible permutations
This can be calculated using the permutation formula:
nPr = n! / (nr)!
The number of possible permutations,
nPr
is6! / (6  3)! = 120
.
For combination, let's assume the following:
 Calculation: Combination
 The total number of objects,
n
:7
 Sample size,
r
:4
You can calculate the number of possible permutation in three steps:
 Determine the total number of objects
The definition of the total number of objects is the same as the one in permutation. In this example,
n
is7
.
 Determine the sample size
Similarly, this is the size of the combinations that you wish to compute. The
r
in this example is4
.
 Calculate the number of possible combinations
This can be calculated using the combination formula:
nCr = n! / (r!(nr)!)
The number of possible combinations,
nCr
is7! / 4! * (7  4)! = 35
.
If the permutations and combinations formula still seems confusing, don't worry, just use our calculator for the calculations. We will even show you the permutation and combinations examples.
What is the difference between permutation and combination?
Now that we understand the definitions of permutations and combinations, let's discuss what the difference between permutation and combination is.
There are two main differences between combination and permutations:

As permutation calculates the number of possible ways to arrange a certain number of items, different sequences with the same items are considered different. For example
ABC
andBCA
are two different permutations. Whereas for combination, they are considered the same. 
Permutation and combination are meant to solve different probability problems. While permutation deals with sequential problems like the lottery, combination are mostly used to solve problem that ignore sequence.
Here are some permutation and combination related calculators
To understand more about this topic, I strongly recommend you to check out our other calculators on this topic:
FAQ
What is combination?
Combination is defined as the number of ways that is possible in grouping n
object in r
size. The order of the items in the group does not matter.
What is permutation?
Permutation is defined as the number of possible ways that in arranging n
object in r
size. The order of the items in the group matters.
How to calculate combination?
You can calculate the combination in three steps:
 Determine the total number of objects,
n
 Determine the sample size,
r
 Apply the combination formula:
nCr = n! / (r!(nr)!)
How to calculate permutation?
You can calculate the permutation in three steps:
 Determine the total number of objects,
n
 Determine the sample size,
r
 Apply the combination formula:
nPr = n! / (nr)!
Can combination and permutation be negative?
No, combination and permutation cannot be negative. Even with one sample, the combination and permutation should be at least 1.