Evaluate the combination:
40C4
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 = 4
| 40C4 2 | 40! |
| 4!(40 - 4)! |
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 - 4)!
(40 - 4)! = 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! = 4!
4! = 4 x 3 x 2 x 1
4! = 24
Calculate 40C4
| 40C4 = | 815,915,283,247,897,683,795,548,521,301,193,790,359,984,930,816 |
| 24 x 371,993,326,789,901,177,492,420,297,158,468,206,329,856 |
| 40C4 = | 815,915,283,247,897,683,795,548,521,301,193,790,359,984,930,816 |
| 8,927,839,842,957,628,259,818,087,131,803,236,951,916,544 |
40C4 = 91,390
You have 1 free calculations remaining
Excel or Google Sheets formula:
Excel or Google Sheets formula:=COMBIN(40,4)
What is the Answer?
40C4 = 91,390
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?
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
