Evaluate the combination:
10C6
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 = 6
| 10C6 2 | 10! |
| 6!(10 - 6)! |
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 - 6)!
(10 - 6)! = 4!
4! = 4 x 3 x 2 x 1
4! = 24
Calculate r!:
r! = 6!
6! = 6 x 5 x 4 x 3 x 2 x 1
6! = 720
Calculate 10C6
| 10C6 = | 3,628,800 |
| 720 x 24 |
| 10C6 = | 3,628,800 |
| 17,280 |
10C6 = 210
Excel or Google Sheets formula:
Excel or Google Sheets formula:=COMBIN(10,6)Common Core State Standards In This Lesson
HSS.CP.B.9
What is the Answer?
10C6 = 210
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.
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)!
nCr=n!/r!(n-r)!
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
