Enter your n and r values below:

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

  

Evaluate the combination:

7C4

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 = 7 and r = 4

7C4  2  7!
  4!(7 - 4)!

Factorial Formula:

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

Calculate the numerator n!:

n! = 7!

7! = 7 x 6 x 5 x 4 x 3 x 2 x 1

7! = 5,040

Calculate (n - r)!:

(n - r)! = (7 - 4)!

(7 - 4)! = 3!

3! = 3 x 2 x 1

3! = 6

Calculate r!:

r! = 4!

4! = 4 x 3 x 2 x 1

4! = 24

Calculate 7C4

7C4  =  5,040
  24 x 6

7C4  =  5,040
  144

7C4 = 35




Excel or Google Sheets formula:

Excel or Google Sheets formula:=COMBIN(7,4)


What is the Answer?
7C4 = 35
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
Permutations and Combinations Calculator Video

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