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.
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
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
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. Refer the below table for example input & output of permutations calculator. It's usually represented by nPr and calculated from the below formula nPr = n!/(n - r)!
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. Refer the below table for example input & output of n-choose-k calculator. It's usually represented by nCr and calculated from the below formula nCr = n!/(r!(n - r)!)
|2 choose 1||2|
|3 choose 1||3|
|3 choose 2||3|
|4 choose 1||4|
|4 choose 2||6|
|4 choose 3||4|
|5 choose 1||5|
|5 choose 2||10|
|5 choose 3||10|
|5 choose 4||5|
|6 choose 1||6|
|6 choose 2||15|
|6 choose 3||20|
|6 choose 4||15|
|6 choose 5||6|
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.
|Worksheet for how to Calculate Permutations nPr and Combination nCr|