23 Combinations of 3
Evaluate the combination:
23C3
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 = 23 and r = 3
| 23C3 2 | 23! |
| 3!(23 - 3)! |
Factorial Formula:
n! = n * (n - 1) * (n - 2) * .... * 2 * 1
Calculate the numerator n!:
n! = 23!
23! = 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
23! = 25,852,016,738,884,978,212,864
Calculate (n - r)!:
(n - r)! = (23 - 3)!
(23 - 3)! = 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 r!:
r! = 3!
3! = 3 x 2 x 1
3! = 6
Calculate 23C3
| 23C3 = | 25,852,016,738,884,978,212,864 |
| 6 x 2,432,902,008,176,640,000 |
| 23C3 = | 25,852,016,738,884,978,212,864 |
| 14,597,412,049,059,840,000 |
23C3 = 1,771
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Excel or Google Sheets formula:
Excel or Google Sheets formula:=COMBIN(23,3)What is the Answer?
23C3 = 1,771
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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