Evaluate the combination:
10C5
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 = 10 and r = 5
| 10C5 2 | 10! |
| 5!(10 - 5)! |
Factorial Formula:
n! = n * (n - 1) * (n - 2) * .... * 2 * 1
Calculate the numerator n!:
n! = 10!
10! = 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1
10! = 3,628,800
Calculate (n - r)!:
(n - r)! = (10 - 5)!
(10 - 5)! = 5!
5! = 5 x 4 x 3 x 2 x 1
5! = 120
Calculate r!:
r! = 5!
5! = 5 x 4 x 3 x 2 x 1
5! = 120
Calculate 10C5
| 10C5 = | 3,628,800 |
| 120 x 120 |
| 10C5 = | 3,628,800 |
| 14,400 |
10C5 = 252
Excel or Google Sheets formula:
=COMBIN(10,5)What is the Answer?
10C5 = 252
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?
combinationa mathematical technique that determines the number of possible arrangements in a collection of items where the order of the selection does not matternPr = n!/r!(n - r)!factorialThe product of an integer and all the integers below itpermutationa way in which a set or number of things can be ordered or arranged.
nPr = n!/(n - r)!permutations and combinations
Example calculations for the Permutations and Combinations Calculator
Permutations and Combinations Calculator Video
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