Evaluate the combination:
37C7
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 = 37 and r = 7
| 37C7 2 | 37! |
| 7!(37 - 7)! |
Factorial Formula:
n! = n * (n - 1) * (n - 2) * .... * 2 * 1
Calculate the numerator n!:
n! = 37!
37! = 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
37! = 13,763,753,091,226,343,102,992,036,262,845,720,547,033,088
Calculate (n - r)!:
(n - r)! = (37 - 7)!
(37 - 7)! = 30!
30! = 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
30! = 265,252,859,812,191,032,188,804,700,045,312
Calculate r!:
r! = 7!
7! = 7 x 6 x 5 x 4 x 3 x 2 x 1
7! = 5,040
Calculate 37C7
| 37C7 = | 13,763,753,091,226,343,102,992,036,262,845,720,547,033,088 |
| 5,040 x 265,252,859,812,191,032,188,804,700,045,312 |
| 37C7 = | 13,763,753,091,226,343,102,992,036,262,845,720,547,033,088 |
| 1,336,874,413,453,442,836,819,220,826,433,781,760 |
37C7 = 10,295,472
You have 1 free calculations remaining
Excel or Google Sheets formula:
Excel or Google Sheets formula:=COMBIN(37,7)
What is the Answer?
37C7 = 10,295,472
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
