Evaluate the combination:
38C2
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 = 38 and r = 2
| 38C2 2 | 38! |
| 2!(38 - 2)! |
Factorial Formula:
n! = n * (n - 1) * (n - 2) * .... * 2 * 1
Calculate the numerator n!:
n! = 38!
38! = 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
38! = 523,022,617,466,601,037,913,697,377,988,137,380,787,257,344
Calculate (n - r)!:
(n - r)! = (38 - 2)!
(38 - 2)! = 36!
36! = 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
36! = 371,993,326,789,901,177,492,420,297,158,468,206,329,856
Calculate r!:
r! = 2!
2! = 2 x 1
2! = 2
Calculate 38C2
| 38C2 = | 523,022,617,466,601,037,913,697,377,988,137,380,787,257,344 |
| 2 x 371,993,326,789,901,177,492,420,297,158,468,206,329,856 |
| 38C2 = | 523,022,617,466,601,037,913,697,377,988,137,380,787,257,344 |
| 743,986,653,579,802,354,984,840,594,316,936,412,659,712 |
38C2 = 703
You have 1 free calculations remaining
Excel or Google Sheets formula:
Excel or Google Sheets formula:=COMBIN(38,2)
What is the Answer?
38C2 = 703
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
