`"Comparisons" = "n" ^2 - "n" `

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This computes the number of comparison pair where you have n things to choose pairs from without comparing to itself. Ex. We want all conversions between set of 'n' units. Units A, B, C, D, E. The number of permutations of these comparisons is the number in an n X n matrix minus the diagonals

 

Calculator Key: `P_"comp"(n,2)`

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