Different Permutation (nPr) & Combination (nCr) Calculator

Permutation P(n,r) & Combination C(n,r) Calculation

N =  (Sample Points in Set)
R =  (Sample Points)

permutation & combination calculator - step by step calculation to find number of different permutations nPr & combinations nCr provided along with meaning, formula & solved example problems for statistics data analysis. Users can get the complete step by step calculation for each calculation they do by using this calculator. nPr - permutation calculator finds the number of different permutations of n distinct objects taken r at a time where as the nCr calculator finds the number of different combinations of n distinct objects taken r at a time. The factorial of number calculation one of the primary part in both permutation & combination calculation.

formulas

The below mathematical formulas are used to find the different number of permutations P(n,r) & combinations C(n,r) of n distinct objects taken r at a time

Solved Example Problem

The below solved example problem may useful to understand how the values are being used in permutations P(n,r) & combinations C(n,r) calculation by using the above formulas.

Example Problem
Find the number of different permutations nPr & combinations nCr of a box containing 6 distinct colour balls taken 3 at a time?

Solution
Data given
n = 6
r = 3

Step by step calculation
formula to find permutation nPr = n!/(n-r)!
n! = 6! = 6 x 5 x 4 x 3 x 2 x 1
n! = 720

(n - r)! = 3! = 3 x 2 x 1
(n - r)! = 6

r! = 3! = 3 x 2 x 1
r! = 6

substitute the values
= 720/6
nPr = 120

formula to find permutation nCr = n!/(r!(n-r)!)
substitute the above values
= 720/(6 x 6)
nCr = 20

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 different 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 distinct objects. A r-permutation of n objects is a permutation of r of them. There are n!/(n - r)! different r - permutations of n symbols. It's usually represented by nPr and calculated from the below 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. It's usually represented by nCr and calculated from the below 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 is 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

In many applications in the field of probability & statistics, finding the permutations & combinations is very important to analyse and summarize the statistical data. The above formulas, step by step calculation & example solved problem help users to understand how the values are being used in nPr & nCr calculations and how to be done such calculations manually but, when it comes to online for quick computations, this permutation & combination calculator help users to workout, perform & verify such calculations as quick as possible.

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