Evaluate the combination:
17C3
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 = 17 and r = 3
| 17C3 2 | 17! |
| 3!(17 - 3)! |
Factorial Formula:
n! = n * (n - 1) * (n - 2) * .... * 2 * 1
Calculate the numerator n!:
n! = 17!
17! = 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
17! = 355,687,428,096,000
Calculate (n - r)!:
(n - r)! = (17 - 3)!
(17 - 3)! = 14!
14! = 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
14! = 87,178,291,200
Calculate r!:
r! = 3!
3! = 3 x 2 x 1
3! = 6
Calculate 17C3
| 17C3 = | 355,687,428,096,000 |
| 6 x 87,178,291,200 |
| 17C3 = | 355,687,428,096,000 |
| 523,069,747,200 |
17C3 = 680
Excel or Google Sheets formula:
=COMBIN(17,3)
What is the Answer?
17C3 = 680
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
