Permutation and Combination Calculator
A permutation is a technique that determines the number of possible arrangements in a set when the order of the arrangements matters. A combination is a mathematical technique that determines the number of possible arrangements in a collection of items where the order of the selection does not matter.
What is Permutation and Combination Calculator?
'Cuemath's Permutation and Combination Calculator' is an online tool that helps to calculate the number of possible permutations and combinations. Cuemath's online Permutation and Combination Calculator helps you to calculate the number of possible permutations and combinations in a few seconds.
Note: Enter the input values up to five digits only.
How to Use Permutation and Combination Calculator?
Please follow the steps below on how to use the calculator:
- Step 1: Choose a drop-down list to calculate for permutations and combinations
- Step 2: Enter the total number of objects, and the sample size in the given input boxes.
- Step 3: Click on the "Calculate" button to find the number of possible permutations and combinations.
- Step 4: Click on the "Reset" button to clear the fields and enter the different values.
How to Find Permutation and Combination?
The permutations are defined as the number of possible ways to select a subset (r) from a larger set of objects (n), however the order of subset matters here. To determine the number of Permutation the following formula is used:
P(n,r) = n!/(n-r)!
It is read as the number of possible Permutation of selecting a subset 'r' from 'n' distinct objects.
The combinations are defined as the number of ways in which a sample of r elements can be selected from n distinct objects that's why it is also referred as 'n choose r'. To determine the number of combinations the following formula is used:
C(n,r) = n! / (r!(n - r)!)
It is read as the number of possible combinations of selecting a sample 'r' from 'n' distinct objects.
Solved Examples on Permutations and Combinations Calculator
Find the number of ways in which the top 3 players can be ranked from a pool of 6 players.
Total number of players (n) = 6
Required subset size = 3
Number of possible permutations = P(n,r) = n!/(n-r)!
P(6,3) = 6!/(6-3)!
P(6,3) = 6!/(3)!
P(6,3) = 120.
Find the number of ways in which 6 balls can be selected from a bag containing 9 different colored balls
Total number of balls = 9
Required Sample size = 6
Number of combinations = C(n,r) = n!/(r!(n-r)!)
C(9,6) = 9!/(6!(9-6)!)
C(9,6) = 9!/(6!(3)!)
C(9,6) = 84.
Similarly, you can use the calculator to find the permutations and combinations for:
- Number of objects = 10 and sample size = 5
- Number of objects = 15 and sample size = 3