Evaluate the combination:
40C2
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 = 40 and r = 2
| 40C2 2 | 40! |
| 2!(40 - 2)! |
Factorial Formula:
n! = n * (n - 1) * (n - 2) * .... * 2 * 1
Calculate the numerator n!:
n! = 40!
40! = 40 x 39 x 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
40! = 815,915,283,247,897,683,795,548,521,301,193,790,359,984,930,816
Calculate (n - r)!:
(n - r)! = (40 - 2)!
(40 - 2)! = 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 r!:
r! = 2!
2! = 2 x 1
2! = 2
Calculate 40C2
| 40C2 = | 815,915,283,247,897,683,795,548,521,301,193,790,359,984,930,816 |
| 2 x 523,022,617,466,601,037,913,697,377,988,137,380,787,257,344 |
| 40C2 = | 815,915,283,247,897,683,795,548,521,301,193,790,359,984,930,816 |
| 1,046,045,234,933,202,075,827,394,755,976,274,761,574,514,688 |
40C2 = 780
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Excel or Google Sheets formula:
Excel or Google Sheets formula:=COMBIN(40,2)
What is the Answer?
40C2 = 780
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
