PERM Function

Computes the number of permutations of n items that are taken r at a time.

Category:

Combinatorial

Syntax

PERM(n<,r> )

Required Argument

n

is an integer that represents the total number of elements from which the sample is chosen.

Optional Argument

r

is an integer value that represents the number of chosen elements. If r is omitted, the function returns the factorial of n.

Restriction

r ≤ n

Details

The mathematical representation of the PERM function is given by the following equation:

\begin{matrix} P E R M (n, r) = \frac{n!}{(n - r)!} \end{matrix}

with n ≥ 0, r ≥ 0, and n≥ r.

If the expression cannot be computed, a missing value is returned. For moderately large values, it is sometimes not possible to compute the PERM function.

Example

The following SAS statements produce these results.

SAS Statement	Result
x=perm(5,1);	5
x=perm(5);	120
x=perm(5,2)	20