Evaluate the combination:
27C2
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 = 27 and r = 2
| 27C2 2 | 27! |
| 2!(27 - 2)! |
Factorial Formula:
n! = n * (n - 1) * (n - 2) * .... * 2 * 1
Calculate the numerator n!:
n! = 27!
27! = 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
27! = 10,888,869,450,418,351,940,239,884,288
Calculate (n - r)!:
(n - r)! = (27 - 2)!
(27 - 2)! = 25!
25! = 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
25! = 15,511,210,043,330,986,055,303,168
Calculate r!:
r! = 2!
2! = 2 x 1
2! = 2
Calculate 27C2
| 27C2 = | 10,888,869,450,418,351,940,239,884,288 |
| 2 x 15,511,210,043,330,986,055,303,168 |
| 27C2 = | 10,888,869,450,418,351,940,239,884,288 |
| 31,022,420,086,661,972,110,606,336 |
27C2 = 351
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Excel or Google Sheets formula:
Excel or Google Sheets formula:=COMBIN(27,2)What is the Answer?
27C2 = 351
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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