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Combination Calculator
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If there are n items given and when we have to pick up r items of them, to find all the possible ways, we use the following online combination calculator. Here n stands for the total number of  items and r is for number of choosing options.

The formula to find it out manually is -
nCr = $\frac{n!}{ r! (n - r)!} $ 

Combination Calculator (or Number Combination Calculator) is an online tool which takes Total number of options (n) and number of options to be selected (r) and calculates the possible ways in which selection can be done, when order of selection does not matter.

 

Step by Step Calculation

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Step 1 :  

Formula for combinations nCr =  $\frac{n!}{ r! (n - r)!} $  


Where 0 <=  r <= n .



Step 2 :  

Put the values in the formula and calculate the combinations of the given numbers.



Example Problems

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  1. There are 10 men working in the company. How many ways we can arrange the groups of people, which can accommodate 5 people for each group?


    Step 1 :  

    Formula for combinations nCr = $\frac{n!}{ r! (n - r)!} $


    Here n = 10 and r = 5


    first we need to find out 10! and 5! values.


    10! = 3628800


    5! = 120



    Step 2 :  

    Substitute the factorial values in the formula  nCr = $\frac{n!}{ r! (n - r)!} $ 


    $\frac{10!}{ 5! (10 - 5)!} $ 


    = 252



    Answer  :  

    252



  2. In a public examination question paper each question has 5 options as answers. among them only 2 are the right answers and the rest are wrong answers. How many ways are there for a student to pick up the correct answers for a question.


    Step 1 :  

    Formula for combinations nCr = $\frac{n!}{ r! (n - r)!} $ 


    Here n = 5 and r = 2


    first we need to find out 5! and 2! values.


    5! = 120


    2! = 2



    Step 2 :  

    Substitute the factorial values in the formula  nCr = $\frac{n!}{ r! (n - r)!} $ 


    $\frac{5!}{ 2! (5 - 2)!} $ 


    = 10



    Answer  :  

    10



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