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5 Combinations of 3

Enter your n and r values below:

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

  
Evaluate the combination:
5C3

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 = 5 and r = 3

5C3  2  5!
  3!(5 - 3)!

Factorial Formula:

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

Calculate the numerator n!:

n! = 5!
5! = 5 x 4 x 3 x 2 x 1
5! = 120

Calculate (n - r)!:

(n - r)! = (5 - 3)!
(5 - 3)! = 2!
2! = 2 x 1
2! = 2

Calculate r!:

r! = 3!
3! = 3 x 2 x 1
3! = 6

Calculate 5C3

5C3  =  120
  6 x 2

5C3  =  120
  12




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Excel or Google Sheets formula:

=COMBIN(5,3)


What is the Answer?

5C3 = 10

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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  5. 6 permutation 2
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  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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