Permutation and Combination Calculator

What are Permutation and Combination?

Given a sample size, permutation refers to the number of ways a certain number of objects can be arranged in order. On the other hand, combination refers to the number of ways a certain number of items can be grouped together.
These two concepts are very useful in calculating probability. Have you ever wondered what the probability of winning the lottery is? To win the prize, you need to match the numbers in the correct order. Therefore, to answer this question, you need to understand permutations. Similar concepts also apply to combinations.

How to Calculate Permutations and Combinations? Permutation and Combination Formulas

To understand the calculation of permutations and combinations, let's look at some examples below.
For permutations, assume the following data:
Calculation: Permutation
Total number of objects n: 6
Sample size r: 3
You can calculate the number of possible permutations in three steps:
Determine the total number of objects
This is the total number of items you have. In this example, n is 6.
Determine the sample size
This is the size of the permutation you wish to calculate. In this example, r is 3.
Calculate the number of possible permutations
This can be calculated using the permutation formula:
nPr = n! / (n - r)!
The number of possible permutations nPr is 6! / (6 - 3)! = 120.
For combinations, assume the following data:
Calculation: Combination
Total number of objects n: 7
Sample size r: 4
You can calculate the number of possible combinations in three steps:
Determine the total number of objects
The definition of the total number of objects is the same as in permutations. In this example, n is 7.
Determine the sample size
Similarly, this is the size of the combination you wish to calculate. In this example, r is 4.
Calculate the number of possible combinations
This can be calculated using the combination formula:
nCr = n! / (r! * (n - r)!)
The number of possible combinations nCr is 7! / (4! * (7 - 4)!) = 35.
If the permutation and combination formulas still confuse you, don't worry; simply use our calculator to compute them. We will even show you permutation and combination examples.

What is the Difference Between Permutation and Combination?

Now that we understand the definitions of permutation and combination, let's discuss the differences between them.
There are two main differences between combinations and permutations:
Since permutations calculate the number of possible arrangements of a certain number of elements, different sequences containing the same elements are considered distinct. For example, ABC and BCA are two different permutations. However, for combinations, they are considered the same.
Permutations and combinations are used to solve different probability problems. Permutations are used to solve sequence-related problems like lotteries, while combinations are primarily used to solve problems where the sequence is irrelevant.