18 Combinations of 1

Publish date: 2024-05-27
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Evaluate the combination:

18C1

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 = 18 and r = 1
18C1  2  18!
  1!(18 - 1)!

Factorial Formula:

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

Calculate the numerator n!:

n! = 18!

18! = 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

18! = 6,402,373,705,728,000

Calculate (n - r)!:

(n - r)! = (18 - 1)!

(18 - 1)! = 17!

17! = 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

17! = 355,687,428,096,000

Calculate r!:

r! = 1!

1! = 1

1! = 1

Calculate 18C1
18C1  =  6,402,373,705,728,000
  1 x 355,687,428,096,000

18C1  =  6,402,373,705,728,000
  355,687,428,096,000

18C1 = 18

You have 1 free calculations remaining


Excel or Google Sheets formula:
Excel or Google Sheets formula:=COMBIN(18,1)

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 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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