# A to Z of Excel Functions: The PERMUTATIONA Function

18 September 2023

*Welcome
back to our regular A to Z of Excel Functions blog. Today we look at the PERMUTATIONA function. *

** **

**The
PERMUTATIONA function**

This function returns the number of permutations
for a given number of objects that can be selected from number objects allowing
for repetitions (*i.e.* items selected are then replaced). A permutation is any set or subset of objects
or events where internal order is significant (*i.e.* order is important). Permutations are different from combinations,
for which the internal order is not significant (*i.e. *order is
unimportant).

It is defined as follows:

**PERMUTATIONA = Total ^{Chosen}**

For example, selecting two numbers with replacement out of the set {1, 2, 3, 4} where order is important gives you the following pairs: {1, 1}, {1, 2}, {1, 3}, {1, 4}, {2, 1}, {2, 2}, {2, 3}, {2, 4}, {3, 1}, {3, 2}, {3, 3}, {3, 4}, {4, 1}, {4, 2}, {4, 3} and {4, 4}, which is 16 ordered pairs.

The syntax of the **PERMUTATIONA **function is
as follows:

**=PERMUTATIONA(number,
number_chosen)**

It contains two arguments:

**number:**this is required and represents an integer that describes the number of objects**number_chosen:**this is also required and denotes an integer that describes the number of objects in each permutation.

It should be noted that:

- both arguments are truncated to integers
- if numeric arguments are
values that are not valid,
*e.g.*when the total number is zero [0] and the chosen number is larger than zero[0],**PERMUTATIONA**returns the*#NUM*! error value - if numeric arguments use
data types that are nonnumeric,
**PERMUTATIONA**returns the*#VALUE!*error value.

Please see my examples below:

We’ll continue our A to Z of Excel Functions soon. Keep checking back – there’s a new blog post every business day.

*A full page of the function articles can be found here. *