11 Combinations of 3

Evaluate the combination:
₁₁C₃

Combination Definition:

A unique order or arrangement

Combination Formula:

_nC_r =	n!
	r!(n - r)!

where n is the number of items
r is the unique arrangements.

Plug in n = 11 and r = 3

₁₁C₃ 2	11!
	3!(11 - 3)!

Factorial Formula:

n! = n * (n - 1) * (n - 2) * .... * 2 * 1

Calculate the numerator n!:

n! = 11!
11! = 11 x 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1
11! = 39,916,800

Calculate (n - r)!:

(n - r)! = (11 - 3)!
(11 - 3)! = 8!
8! = 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1
8! = 40,320

Calculate r!:

r! = 3!
3! = 3 x 2 x 1
3! = 6

Calculate ₁₁C₃

₁₁C₃ =	39,916,800
	6 x 40,320

₁₁C₃ =	39,916,800
	241,920

Excel or Google Sheets formula:

=COMBIN(11,3)

What is the Answer?

₁₁C₃ = 165

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 = _nP_r
Number of combination(s) of n items arranged in r unique ways = _nC_r 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?

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
_nP_r = 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.
_nP_r = n!/(n - r)!
permutations and combinations

Example calculations for the Permutations and Combinations Calculator

Permutations and Combinations Calculator Video

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