10 Combinations of 4

Enter your n and r values below:

<-- Enter Number of Items (n)
<-- Enter Number of Arrangements (r)

  

Evalute the combination nCr
A combination is a way to order or arrange a set or number of things (uniquely)
The formula for a combination of choosing r unique ways from n possibilities is:
nCr  =  n!
  r!(n - r)!

where n is the number of items and r is the unique arrangements.

Plugging in our numbers of n = 10 and r = 4, we get:

10C4  =  10!
  4!(10 - 4)!

Remember from our factorial lesson that n! = n * (n - 1) * (n - 2) * .... * 2 * 1

Calculate the numerator n!:

n! = 10!
10! = 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1
10! = 3,628,800

Calculate the first denominator (n - r)!:

(n - r)! = (10 - 4)!
(10 - 4)! = 6!
6! = 6 x 5 x 4 x 3 x 2 x 1
6! = 720

Calculate the second denominator r!:

r! = 4!
4! = 4 x 3 x 2 x 1
4! = 24

Calculate our combination value nCr for n = 10 and r = 4:

10C4  =  3,628,800
  24 x 720

10C4  =  3,628,800
  17,280

10C4 = 210

In Microsoft Excel or Google Sheets, you write this function as =COMBIN(10,4)


Permutations and Combinations Video


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