Permutations

The Permutations calculator computes the number of permutations possible in a set of r elements from a finite set of n objects where, unlike combinations, different orders create different permutations (i.e. where order is important). 

INSTRUCTIONS: Enter the following:

• (n) Total Number of Objects
• (r) Size of Subset 

Permutations (_nP_r): The calculator returns the number of permutations.  This function is a prominent feature with other statistical functions in the College Level Statistics Calculator (Stat Calc).

The Math / Science

The formula for permutations is as follows:

                   _nP_r = `(n!)/((n-r)!)`

The equation computes the number of possible sequences of r elements that can be chose from a set of n elements, where all of the n elements are unique.

EXAMPLE:

As an example if you have seven different objects from which you select three objects the number of permutations is defined as P(7,3).  As you choose the first element you have seven possibilities to choose from.  After choosing the first you have six possibilities remaining to choose the second.  After choosing the second you have five possibilities remaining to choose the third.  So, you multiply those three possibilities for the three choices and get 7 * 6 * 5 choices = P(7,3) = 210.

The r-permutation of a set S of n element is denoted by `""_n P_r` or by P(n,r).

P(n,r) = `n! / (n-r)!`

For n`>=` 0 we define P(n,0) to be 1 and P(n,n) = n!

Combinatorics Calculators

• n! - factorial
• `n!  sqrt(2 pi n) (n/e)^n` - Stirling's factorial approximation
• _nC_k - combinations
• C_r(n,k) - combinations with repetitions
• _nP_k - permutations
• P_r(n) - permutations with repetitions
• P_comp(n,2) - Comparison permutations
• P_c(n,r) - Circular Permutation