18 Combinations of 15 ·

06 Jun 2024, 00:00

18 Combinations of 15 Image to Crop

Evaluate the combination:

18C15

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 = 15

18C15 2	18!
	15!(18 - 15)!

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 - 15)!

(18 - 15)! = 3!

3! = 3 x 2 x 1

3! = 6

Calculate r!:

r! = 15!

15! = 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

15! = 1,307,674,368,000

Calculate 18C15

18C15 =	6,402,373,705,728,000
	1,307,674,368,000 x 6

18C15 =	6,402,373,705,728,000
	7,846,046,208,000

18C15 = 816

You have 1 free calculations remaining

Excel or Google Sheets formula:

Excel or Google Sheets formula:=COMBIN(18,15)

What is the Answer?

18C15 = 816

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

18 Combinations of 15

Evaluate the combination: 18C15 A unique order or arrangement where n is the number of itemsr is the unique arrangements. n! = n * (n - 1) * (n - 2) * .... * 2 * 1 n! = 18! 18! = 18 x 17 x 16 x 15 x 14 x 13 x 12