52 Combinations of 7

Evaluate the combination: 52C7 A unique order or arrangement where n is the number of itemsr is the unique arrangements. n! = n * (n - 1) * (n - 2) * .... * 2 * 1 n! = 52! 52! = 52 x 51 x 50 x 49 x 48 x 47 x 46

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Evaluate the combination:

52C7

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 = 52 and r = 7
52C7  2  52!
  7!(52 - 7)!

Factorial Formula:

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

Calculate the numerator n!:

n! = 52!

52! = 52 x 51 x 50 x 49 x 48 x 47 x 46 x 45 x 44 x 43 x 42 x 41 x 40 x 39 x 38 x 37 x 36 x 35 x 34 x 33 x 32 x 31 x 30 x 29 x 28 x 27 x 26 x 25 x 24 x 23 x 22 x 21 x 20 x 19 x 18 x 17 x 16 x 15 x 14 x 13 x 12 x 11 x 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1

52! = 80,658,175,170,943,876,845,634,591,553,351,679,477,960,544,579,306,048,386,139,594,686,464

Calculate (n - r)!:

(n - r)! = (52 - 7)!

(52 - 7)! = 45!

45! = 45 x 44 x 43 x 42 x 41 x 40 x 39 x 38 x 37 x 36 x 35 x 34 x 33 x 32 x 31 x 30 x 29 x 28 x 27 x 26 x 25 x 24 x 23 x 22 x 21 x 20 x 19 x 18 x 17 x 16 x 15 x 14 x 13 x 12 x 11 x 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1

45! = 119,622,220,865,480,188,574,992,723,157,469,373,503,186,265,858,579,103,744

Calculate r!:

r! = 7!

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

7! = 5,040

Calculate 52C7
52C7  =  80,658,175,170,943,876,845,634,591,553,351,679,477,960,544,579,306,048,386,139,594,686,464
  5,040 x 119,622,220,865,480,188,574,992,723,157,469,373,503,186,265,858,579,103,744

52C7  =  80,658,175,170,943,876,845,634,591,553,351,679,477,960,544,579,306,048,386,139,594,686,464
  602,895,993,162,020,150,069,514,180,986,604,655,869,563,181,917,108,034,338,816

52C7 = 133,784,560


Excel or Google Sheets formula:

=COMBIN(52,7)

What is the Answer?

52C7 = 133,784,560

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?

combinationa 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)!factorialThe product of an integer and all the integers below itpermutationa 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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