PermutationA() Function

Permut and Permutationa Functions

The Excel Permut and Permutationa functions both calculate the number of permutations of a selection of objects from a set.

However, the two functions differ in that the Permut function does not count repetitions whereas the Permutationa function does count repetitions.

For example, in a set of 3 objects, a, b, c, how many permutations of 2 objects are there?

-          The Permut Function returns the result 6 (permutations: ab, ac, ba, bc, ca, cb);

-          The Permutationa function returns the result 9 (permutations: aa, ab, ac, ba, bb, bc, ca, cb, cc).

PermutationA Function

The Excel Permutationa function calculates the number of permutations, with repetitions, of a specified number of objects from a set.

Syntax

The syntax for the PERMUT function in Microsoft Excel is:

=PERMUT( number, chosen )

Parameters or Arguments

number

The number of items.

num_chosen

The number of items in each permutation.

Permutationa Function Examples

In the spreadsheet below, the Excel Permutationa function is used to calculate the number of permutations (with repetitions) of six objects, selected from different sized sets.

 Formulas:

	A
1	=PERMUTATIONA( 6, 6 )
2	=PERMUTATIONA( 7, 6 )
3	=PERMUTATIONA( 10, 6 )
4	=PERMUTATIONA( 49, 6 )

Results:

	A
1	46,656
2	117,649
3	1,000,000
4	13,841,287,201

Notes

►   A permutation is a group of items in which order/sequence matters.

►   If order is not significant, use the COMBIN function.

►   Arguments that contain decimal values are truncated to integers.

►   PERMUT returns a #VALUE! error value if

Ø  The supplied number argument is < 0;

Ø  The supplied number_chosen argument is < 0;

Ø  The supplied number argument is < the number_chosen argument.

►   PERMUT returns #NUM! if the supplied arguments are non-numeric.

References

http://www.excelfunctions.net/excel-permutationa-function.html

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