19 Combinations of 8

19 Combinations of 8

Evaluate the combination:

19C8

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 = 19 and r = 8

19C8  2	19!
	8!(19 - 8)!

Factorial Formula:

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

Calculate the numerator n!:

n! = 19!

19! = 19 x 18 x 17 x 16 x 15 x 14 x 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

19! = 121,645,100,408,832,000

Calculate (n - r)!:

(n - r)! = (19 - 8)!

(19 - 8)! = 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 r!:

r! = 8!

8! = 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1

8! = 40,320

Calculate 19C8

19C8  =	121,645,100,408,832,000
	40,320 x 39,916,800

19C8  =	121,645,100,408,832,000
	1,609,445,376,000

19C8 = 75,582

You have 1 free calculations remaining

Excel or Google Sheets formula:

Excel or Google Sheets formula:=COMBIN(19,8)

What is the Answer?

19C8 = 75,582

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 matter
nPr = 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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