Today I have two functions I would like to demonstrate, they calculate all possible combinations from a cell range. What is a combination? To explain combinations I must explain the difference between combinations and permutations.

Think of permutations as if the order is important and combinations as if the order is not important. If this is confusing, look at the following examples.

Example 1 - Permutations

phone_sThink of a phone number, each digit can be between 0 to 9 or 10 different values. A five digit phone number contains 100 000 permutations (10x10x10x10x10 equals 100 000).

Now imagine a phone number to a friend or co-worker. If we rearrange the phone numbers, you could possibly call a stranger. The order is important.

Read this article to learn more about permutations:

Permutations with and without repetition

I discussed the difference between permutations and combinations in my last post, today I want to talk about two kinds […]

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Example 2 - Combinations

pizza-slice1Imagine you are about to buy a pizza and you can choose from five ingredients, cheese, tomato sauce, onions, ham and mushrooms. It doesn´t matter in what order you say the ingredients. The order is not important.

A five digit phone number has 100 000 possible permutations but five out of five pizza ingredients has only one combination. I guess only mathematicians use the word permutations, everyone else use the word combinations even if they talk about permutations.

The following article demonstrates a problem solved with combinations, order is not important:

Identify numbers in sum using solver

Here is a useful feature I recently found googling for Excel solver examples. I have summed some random values from […]

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User defined functions

The following function lets you for example see all the combinations of pizza ingredients you can choose from if you pick 5 out of 7 ingredients.

combinations1

Custom array formula in cell range E3:I23:

=Combinations(B3:B9,5)

How to enter an array formula

  1. Select cell range E3:I23
  2. Click in fomula bar
  3. Enter custom function
  4. Press and hold CTRL + SHIFT
  5. Press Enter

If you did it right the formula now begins and ends with curly brackets, like this {=array formula}. They appear automatically, don´t enter the curly brackets yourself.

Learn the basics of Excel arrays

Array formulas allows you to do advanced calculations not possible with regular formulas.

Comments(2) Filed in category: Count values, Excel

VBA Code

Public result() As Variant

Function Combinations(rng As Range, n As Single)
rng1 = rng.Value

ReDim result(n - 1, 0)

Call Recursive(rng1, n, 1, 0)

ReDim Preserve result(UBound(result, 1), UBound(result, 2) - 1)
Combinations = Application.Transpose(result)

End Function

Function Recursive(r As Variant, c As Single, d As Single, e As Single)
Dim f As Single

For f = d To UBound(r, 1)

result(e, UBound(result, 2)) = r(f, 1)

If e = (c - 1) Then

ReDim Preserve result(UBound(result, 1), UBound(result, 2) + 1)

For g = 0 To UBound(result, 1)
result(g, UBound(result, 2)) = result(g, UBound(result, 2) - 1)
Next g
Else
Call Recursive(r, c, f + 1, e + 1)
End If

Next f

End Function

These functions have a limit of 65532 rows, if you need more read this comment.

Where to copy vba code?

  1. Go to VB Editor (Alt + F11)
  2. Click "Insert" on the menu
  3. Click "Module"
  4. Paste code to code module
  5. Return to excel

save multiple excel sheets to a single pdf file3

Tip! Did you know that excel can calculate the number of combinations for you? Use the COMBIN function:

=COMBIN(7,5) equals 21 combinations.

Recommended reading

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Excel udf: List permutations with repetition

This blog post describes how to create permutations. Repetition is allowed. Vba code: Function ListPermut(num As Integer) 'Permutations with repetition […]

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Download excel *.xlsm file

Combinations.xlsm