Evaluate the combination:
13C10
Combination Definition:
A unique order or arrangement
Combination Formula:
| nCr = | n! |
| r!(n - r)! |
where n is the number of itemsr is the unique arrangements.
Plug in n = 13 and r = 10
| 13C10 2 | 13! |
| 10!(13 - 10)! |
Factorial Formula:
n! = n * (n - 1) * (n - 2) * .... * 2 * 1
Calculate the numerator n!:
n! = 13!
13! = 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
13! = 6,227,020,800
Calculate (n - r)!:
(n - r)! = (13 - 10)!
(13 - 10)! = 3!
3! = 3 x 2 x 1
3! = 6
Calculate r!:
r! = 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 13C10
| 13C10 = | 6,227,020,800 |
| 3,628,800 x 6 |
| 13C10 = | 6,227,020,800 |
| 21,772,800 |
13C10 = 286
Table of Contents
Excel or Google Sheets formula:
=COMBIN(13,10)
What is the Answer?
13C10 = 286
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 = nPrNumber of combination(s) of n items arranged in r unique ways = nCr including subsets of setsThis 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 matternPr = 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
