49 Combinations of 6

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Evaluate the combination:

49C6

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 = 49 and r = 6
49C6  2  49!
  6!(49 - 6)!

Factorial Formula:

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

Calculate the numerator n!:

n! = 49!

49! = 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

49! = 608,281,864,034,267,522,488,601,608,116,731,623,168,777,542,102,418,391,010,639,872

Calculate (n - r)!:

(n - r)! = (49 - 6)!

(49 - 6)! = 43!

43! = 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

43! = 60,415,263,063,373,834,074,440,829,285,578,945,930,237,590,418,489,344

Calculate r!:

r! = 6!

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

6! = 720

Calculate 49C6
49C6  =  608,281,864,034,267,522,488,601,608,116,731,623,168,777,542,102,418,391,010,639,872
  720 x 60,415,263,063,373,834,074,440,829,285,578,945,930,237,590,418,489,344

49C6  =  608,281,864,034,267,522,488,601,608,116,731,623,168,777,542,102,418,391,010,639,872
  43,498,989,405,629,158,491,903,195,559,986,060,289,523,420,510,703,058,944

49C6 = 13,983,816

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Excel or Google Sheets formula:
Excel or Google Sheets formula:=COMBIN(49,6)

What is the Answer?

49C6 = 13,983,816

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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