23 Combinations of 2
Ava Arnold
Published Jan 20, 2026
Evaluate the combination:
23C2
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 = 2
| 23C2 2 | 23! |
| 2!(23 - 2)! |
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 - 2)!
(23 - 2)! = 21!
21! = 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
21! = 51,090,942,171,709,440,000
Calculate r!:
r! = 2!
2! = 2 x 1
2! = 2
Calculate 23C2
| 23C2 = | 25,852,016,738,884,978,212,864 |
| 2 x 51,090,942,171,709,440,000 |
| 23C2 = | 25,852,016,738,884,978,212,864 |
| 102,181,884,343,418,880,000 |
23C2 = 253
You have 1 free calculations remaining
Excel or Google Sheets formula:
Excel or Google Sheets formula:=COMBIN(23,2)
What is the Answer?
23C2 = 253
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?
- combination
- a 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)! - factorial
- The product of an integer and all the integers below it
- permutation
- a way in which a set or number of things can be ordered or arranged.
nPr = n!/(n - r)! - permutations and combinations
