Combination Calculator (Permutation Calculator)

If you’re a student or somebody who deals with statistics, you should know terms like combinations, permutations, probabilities, and so on. These are important data in statistics and to facilitate solving these, you can make use of a combination calculator. This tool can help you determine how many combinations are there in a certain group or every possible combination of such group.

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How to use the combination calculator?

This combination or permutation calculator is a simple tool which gives you the combinations you need. You can also use the nCr formula to calculate combinations but this online tool is much easier. Here are the steps to follow when using this combination formula calculator:

  • On the left side, enter the values for the Number of Objects (n) and the Sample Size (r).
  • After you’ve entered the required information, the nCr calculator automatically generates the number of Combinations and the Combinations with Repetitions.
  • The calculator also serves as a Combination Generator where it shows you all of the objects when you make a selection from the drop-down menu.

How do you calculate combinations?

In statistics, how would you define a combination? It’s a selection of all or part of a set of objects, without regard to the order in which objects get selected. Let’s use an example to illustrate this. Suppose you have a set of 3 letters, namely E, F, and G.

How many possible combinations are there if we consider just 2 letters from this set? We can have EF, EG, and FG. When counting the number of combinations, we don’t have to consider the order. This means that EF is the same as FE. However, if you consider the order, then it means that we’re dealing with permutations where EF is different from FE.

The previous example deals with only 3 elements in the set. With such a small number, you can easily identify the combinations without using the combination calculator. But what do you do if you have a big number of elements? The process of listing each could become tedious and confusing.

Fortunately, when given such a set, you can solve the number of combinations mathematically using the nCr formula:

C(n,r) = n!/(r! * (n-r)!)

C(n,r) refers to the number of combinations
n refers to the total number of items in the set,
r refers to the number of items chosen from the set.
! represents a factorial

How do you calculate nCr?

In statistics, a combination refers to how many ways to choose from a set of “r” elements from a set of “n” elements. The order doesn’t matter and any replacements aren’t allowed. The nCr formula is:

nCr = n!/(r! * (n-r)!) where n ≥ r ≥ 0

This formula will give you the number of ways you can combine a certain “r” sample of elements from a set of “n” elements. Again, there is no regard for order and repetitions or replacements aren’t allowed when it comes to combinations. Another definition of combination is “the number of ways of picking ‘r’ unordered outcomes from ‘n’ possibilities.”

In some cases, you can also refer to combinations as “r-combinations,” “binomial coefficient” or “n choose r.” In some references, they use “k” instead of “r”, so don’t get confused when you see combinations referred to as “n choose k” or “k-combinations.”

How do you calculate combinations in Excel?

If you’re using a computer, you can also solve for the number of combinations, in any order, of a given number of elements. To do this, use Microsoft Excel, one of the most common types of word processing software available. Here, you use the COMBIN function. This refers to the number of elements in a set and the “number chosen,” which is the number of elements in every combination. You express the COMBIN function as:

COMBIN = (n,r)

n refers to the number of elements
r refers to the chosen number for each combination.

Briefly defined, a combination is any group of elements in any order. Here are some things you need to know when dealing with combinations using Excel:

  • If you have to take the order of the elements into account, then you must use the PERMUT function instead of the COMBIN function.
  • Arguments which contain decimals get truncated to integers.
  • If the argument isn’t numeric, COMBIN will return a #VALUE! error value. In such a case, check the value you’ve entered.
  • If the number is less than the number chosen, COMBIN will return #NUM!. Again, check the value you’ve entered when you get this result.

How do you calculate permutations?

A permutation is a way, especially one of several possible variations, in which you can arrange or order a set or number of elements. This is perhaps the simplest way to define it. Keep in mind that the key word here is “order” as opposed to combinations where you don’t consider the order.

For instance, if you have to arrange “r” number of elements in a set which contains “n” elements, then you would use a permutation formula. In statistics, we call this example “r-permutations” of “n.” If you don’t use the permutation calculator, you can perform the manual computation using this formula:

P(n,r) = n!/(n-r)!

P(n,r) refers to the number of permutations
n refers to the total number of elements in the set,
r refers to the number of elements you choose from this set.
! represents a factorial

The two equations for permutations and combinations almost look similar. You can simplify the permutation equation by substitution where you would come up with this equation:

P(n,r) = C(n,r) * r!

When to use either the combination or permutation formula will depend on whether you have to take into consideration order or not.

How do you calculate nPr?

As aforementioned, the only difference between a combination and permutation is in the order. Combinations have no regard for this while permutations do. When “n” is equal to “r,” the equation gets reduced to n! which is a simple factorial of n.

nPr = n!/(n−r)! where n ≥ r ≥ 0

To calculate the number of permutations for an ordered subset of “r” elements from a set of “n” elements, the formula is:

nPr = n! / (n – r)!