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Permutation & Combination Calculator is an online statistics tool programmed to calculate the nPr - Permutation and nCr - Combination of the n different items or symbols. The factorial is involved to perform both the ncr and npr calculations for a given N and R sample points of a data set

Permutations

In the context of counting problems, Permutations is the arrangements where the order is important and repetitions or recurrence is not allowed. The number of permutations of n distinct points taken r at a time is written as nPr. Because the number of objects is being arranged cannot exceed total number available. There are n! (n factorial) permutations of n symbols. A r-permutation of n symbols is a permutation of r of them. There are n!/(n - r)! different r-permutations of n symbols. A permutations represented by nPr and calculated from the formula
nPr = n!/(n - r)!

Combinations

The Combinations is a method of selecting several items or symbols out of a larger group or a data set, where an order does not matter. The Combination represented by nCr and calculated from the formula
nCr = n!/(r!(n - r)!)
Each r combination can be arranged in r! different ways. Then the number of r-permutations is equal to the number of r combinations times r!

Factorial

Factorials are used to compute permutations (nPr) and combinations (nCr). A factorial is the result of multiplying a given number of consecutive integers from 1 to the given number. It is written with the exclamation sign: n! and it is defined as
0! = 1
1! = 1
2! = 2 x 1 = 2
3! = 3 x 2 x 1 = 6
4! = 4 x 3 x 2 x 1 = 24
5! = 5 x 4 x 3 x 2 x 1 = 120 and so on

The collection of tools employs the study of methods and procedures used for gathering, organizing, and analyzing data to understand theory of Probability and Statistics. The set of ideas which is intended to offer the way for making scientific implication from such resulting summarized data. In many applications it is necessary to calculate the nPr - Permutation and nCr - Combination for a set of data. With this online Permutation and Combination calculator you can effortlessly make your calculations for the n samples