# Online Combination Calculator (nCr)

## combination Calculator

^{n}c_{r} = n!/(r!*(n-r)!)

## How to use this provided combination calculator tool?

You find the combination with the help of this website where the powerful javascript code is running in the background. Just follow three steps to use this ncr calculator tool:

- In the first block
type a total number of elements in a given set.*[Enter n]* - Then in the second block
enter the smaller number of the group.*[Enter r]* *Finally,*press thebutton.*calculated*

## What is combination in mathematics?

Combination is a mathematical technique that determines the number of possible arrangements in the collection of items when the order of selection doesn’t matter.

**Mathematical Formula:**

Combination ^{n}C_{r} is denoted by

^{n}c_{r} = n!/(r!*(n-r)!)

where,

n= the total number of elements in a set

r= the number of selected objects(the order of the objects is not important)

!= factorial

*The combination ncr is prounced as n chooce r

*In some resources the notation uses “k” instead of “r” .

## Limitation of combination (^{n}C_{r}):

The number of combinations of n different things at a time subject to the restriction that particular things.

- Will never occur
^{n-p}C_{r} - Will always occur
^{n-p}C_{r-p}

### Number of ways of selecting one or more things from a group of n distinct things

^{n}C_{1}+^{n}C_{2}+^{n}C_{3}+………..+^{n}C_{n}=2^{n}-1

### Number of ways of selecting zero or more things from a group of n distinct things

^{n}C_{0}+^{n}C_{1}+^{n}C_{2}+………..+^{n}C_{n}=2^{n}

### Points to remember in combination calculation:

- Order is not important
^{n}c_{r}= n!/(r!*(n-r)!)- Clue word: group, sample, and selection
^{n}c_{k}= n!/(k!*(n-k)!)

*If you found any mistake in online ncr calculator tool or you want to improve my tool then please fill free to contact me.*

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