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Combination Calculator


Online Combination Calculator

Combination calculator helps allows you to find the total possible ways an item is selected from the collection of distinct objects. Our online combination calculator selection of an item is random. To find the number combination, you need to enter the total number of items and the number of items to select.

Combination definition:

A combination is a process of selecting an item from a set of objects. It determines the total possible ways an item is selected but the selection is not in order. The combination is denoted as n C r, C n, r, C (n, r). We can find a combination of the lock to open a combination lock with a sample size of numbers or letters. If we analyse permutations and combinations formula we can say permutations are always greater then combinations.

Combination Formula or Notation:

n C r = n! / (n-r)! r!
It represents that from the total "n" element we can select "r" elements.

Factorial:

Factorial is "!" positive integer value is written to its multiplying in decreasing order.
Example: 4! = 4 X 3 X 2 X 1.

To understand combinations better we examine an example.

Example:

Calculate all possible combinations to form two-digit numbers from the set of 1, 2, 3, 4 numbers? 

We have four numbers 1, 2, 3, 4 then we need to select two numbers at a time. So to determine the number of combinations we have
The total numbers (n) = 4
The total numbers we need select (r) = 2 then we have a formula for the number of combinations is
C (n, r) = n! / (n-r)! r!
C (n, r) = 4! / (4-2)! 2!
C (n, r) = 4! / 2! X 2!
C (n, r) = 6 
So the total possible combination to select two digits numbers is 6.

Instructions to use our tool:

Open combination calculator.
Enter n, r values.
Click on calculate to get possible combinations.