54 Combinations of 6
Evaluate the combination:
54C6
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 = 54 and r = 6
| 54C6 2 | 54! |
| 6!(54 - 6)! |
Factorial Formula:
n! = n * (n - 1) * (n - 2) * .... * 2 * 1
Calculate the numerator n!:
n! = 54!
54! = 54 x 53 x 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
54! = 230,843,697,339,241,379,243,718,839,060,267,085,502,544,784,965,628,964,557,765,331,531,071,488
Calculate (n - r)!:
(n - r)! = (54 - 6)!
(54 - 6)! = 48!
48! = 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
48! = 12,413,915,592,536,072,528,327,568,319,343,857,274,511,609,591,659,416,151,654,400
Calculate r!:
r! = 6!
6! = 6 x 5 x 4 x 3 x 2 x 1
6! = 720
Calculate 54C6
| 54C6 = | 230,843,697,339,241,379,243,718,839,060,267,085,502,544,784,965,628,964,557,765,331,531,071,488 |
| 720 x 12,413,915,592,536,072,528,327,568,319,343,857,274,511,609,591,659,416,151,654,400 |
| 54C6 = | 230,843,697,339,241,379,243,718,839,060,267,085,502,544,784,965,628,964,557,765,331,531,071,488 |
| 8,938,019,226,625,972,266,067,775,356,518,293,431,513,509,928,378,623,993,439,059,968 |
54C6 = 25,827,165
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Excel or Google Sheets formula:
Excel or Google Sheets formula:=COMBIN(54,6)What is the Answer?
54C6 = 25,827,165
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 matternPr = 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
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