Author: Oscar Cronquist Article last updated on December 23, 2018

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 Think 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.

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 […]

### Example 2 - Combinations Imagine 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:

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### User defined functions

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

Custom array formula in cell range E3:I23:

=Combinations(B3:B9,5)

You need to copy the VBA code below to your workbook before you try the above User Defined Function.

https://youtu.be/lZcKDfJ-HoE

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.

How to enter an array formula

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

### 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

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

=COMBIN(7,5) equals 21 combinations.

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