# Combinations and Permutations

You might refer to the characters in a password or the digits on a padlock as a combination. Strictly speaking, this isn’t true though, as the position of each letter, number or symbol is significant, so it’s actually a permutation.

Excel has two functions for combinations and the same number for permutations. All four have the same arguments:

COMBIN/COMBINA/PERMUT/PERMUTATIONA (𝗻𝘂𝗺𝗯𝗲𝗿, 𝗻𝘂𝗺𝗯𝗲𝗿_𝗰𝗵𝗼𝘀𝗲𝗻)

• 𝗻𝘂𝗺𝗯𝗲𝗿 — the number of items

• 𝗻𝘂𝗺𝗯𝗲𝗿_𝗰𝗵𝗼𝘀𝗲𝗻 — the number of items in each combination/permutation

COMBIN and PERMUT 𝘦𝘹𝘤𝘭𝘶𝘥𝘦 repetitions, whereas COMBINA and PERMUTATIONA 𝘪𝘯𝘤𝘭𝘶𝘥𝘦 them.

Let’s have a look at the examples in the document.

## Combinations

COMBIN finds how many combinations can be made with three coloured balls out of a possible four. Without repeating any, it’s impossible to have more combinations than the total items, so a #NUM! error occurs next to those greater than four. (Page 2)

Just by changing the function to COMBINA, it dramatically increases the combinations to 20. That’s because the likes of red–red–blue, green–green–blue and yellow–yellow–yellow are counted. (Page 3)

## Permutations

Both examples focus on how many permutations can be created with any two balls from the four.

Order matters, so PERMUT recognises red–blue and blue–red as separate entities. #NUM! is also returned for any number above four. (Page 4)

PERMUTATIONA allows repetitions, which means results increase exponentially. I remember as a child sitting in a maths lesson amazed how many there could be with such tiny numbers! (Page 5)

#excel