`P_c(n,r) = ( "n" !) / ( "r" ( "n" - "r" )!)`

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

INSTRUCTIONS: Enter the following:

• (n) The total number of objects in the circle.
• (r) The size of the subset 

Circular Permutations: The calculator computes and return the number of circular permutations  P_c(n,r).

The Math

The formula for circular permutations is as follows:

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

This equation computes the number of circular ordered arrangements of r distinct elements for a set of n elements. For example, the number of ways to arrange 5 children in a circle choosing from a group of n children.

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 r-Permutations of n Elements 

Permutations

• Permutations:                                _nP_r = ` (n!)/((n-r)!)`
• Circular Permutations:                 P_c(n,r) = ` (n!)/(r(n-r)!)`
• Permutations with repetitions:     P_r(n) = n^r

Combinations

• Combinations:                                    _nC_k= ` (n!)/(k!(n-k)!)`
• Combinations with repetitions:      C_r(n, k) = ` ((n+k-1)!)/(k!(n-1)!)`