Evaluate the combination:
20C6
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 = 20 and r = 6
| 20C6 2 | 20! |
| 6!(20 - 6)! |
Factorial Formula:
n! = n * (n - 1) * (n - 2) * .... * 2 * 1
Calculate the numerator n!:
n! = 20!
20! = 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
20! = 2,432,902,008,176,640,000
Calculate (n - r)!:
(n - r)! = (20 - 6)!
(20 - 6)! = 14!
14! = 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
14! = 87,178,291,200
Calculate r!:
r! = 6!
6! = 6 x 5 x 4 x 3 x 2 x 1
6! = 720
Calculate 20C6
| 20C6 = | 2,432,902,008,176,640,000 |
| 720 x 87,178,291,200 |
| 20C6 = | 2,432,902,008,176,640,000 |
| 62,768,369,664,000 |
20C6 = 38,760
Excel or Google Sheets formula:
=COMBIN(20,6)What is the Answer?
20C6 = 38,760
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
Example calculations for the Permutations and Combinations Calculator
Permutations and Combinations Calculator Video
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