8 Combinations of 2

Enter your n and r values below:

<-- Enter (n)
<-- Enter (r)

  

Evaluate the combination:
8C2

Combination Definition:

A unique order or arrangement

Combination Formula:

nCr  =  n!
  r!(n - r)!

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

Plug in n = 8 and r = 2

8C2  2  8!
  2!(8 - 2)!

Factorial Formula:

n! = n * (n - 1) * (n - 2) * .... * 2 * 1

Calculate the numerator n!:

n! = 8!
8! = 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1
8! = 40,320

Calculate (n - r)!:

(n - r)! = (8 - 2)!
(8 - 2)! = 6!
6! = 6 x 5 x 4 x 3 x 2 x 1
6! = 720

Calculate r!:

r! = 2!
2! = 2 x 1
2! = 2

Calculate 8C2

8C2  =  40,320
  2 x 720

8C2  =  40,320
  1,440




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Excel or Google Sheets formula:

=COMBIN(8,2)


What is the Answer?

8C2 = 28

How does the Permutations and Combinations Calculator work?

Free Permutations and Combinations Calculator - Calculates the following:
Number of permutation(s) of n items arranged in r ways = nPr
Number of combination(s) of n items arranged in r unique ways = nCr including subsets of sets
This calculator has 2 inputs.

What 2 formulas are used for the Permutations and Combinations Calculator?

nPr=n!/r!
nCr=n!/r!(n-r)!

For more math formulas, check out our Formula Dossier

What 4 concepts are covered in the Permutations and Combinations Calculator?

combination
a mathematical technique that determines the number of possible arrangements in a collection of items where the order of the selection does not matter
nPr = n!/r!(n - r)!
factorial
The product of an integer and all the integers below it
permutation
a way in which a set or number of things can be ordered or arranged.
nPr = n!/(n - r)!
permutations and combinations

Example calculations for the Permutations and Combinations Calculator

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  4. 8 combination 2
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  6. 10 permutations of 5
  7. 6P3
  8. 7c4
  9. how many subsets of at least 3 elements can be formed from a set of 4 elements

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