Evaluate the combination:
9C2
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 = 9 and r = 2
9C2 2 | 9! |
2!(9 - 2)! |
Factorial Formula:
n! = n * (n - 1) * (n - 2) * .... * 2 * 1
Calculate the numerator n!:
n! = 9!
9! = 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1
9! = 362,880
Calculate (n - r)!:
(n - r)! = (9 - 2)!
(9 - 2)! = 7!
7! = 7 x 6 x 5 x 4 x 3 x 2 x 1
7! = 5,040
Calculate r!:
r! = 2!
2! = 2 x 1
2! = 2
Calculate 9C2
9C2 = | 362,880 |
2 x 5,040 |
9C2 = | 362,880 |
10,080 |
9C2 = 36
Excel or Google Sheets formula:
=COMBIN(9,2)What is the Answer?
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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