# Online Combination ncr Calculator

## How to use this provided combination ncr 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:

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

## 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 nCr is denoted by

ncr = 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 (nCr):

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

1. Will never occur n-pCr
2. Will always occur n-pCr-p

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

nC1+nC2+nC3+………..+nCn=2n-1

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

nC0+nC1+nC2+………..+nCn=2n

### Points to remember in combination calculation:

• Order is not important
• ncr = n!/(r!*(n-r)!)
• Clue word: group, sample, and selection
• nck = n!/(k!*(n-k)!)