16 Combinations of 4 ·

11 Jun 2024, 00:00

Evaluate the combination:

16C4

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 = 16 and r = 4

16C4 2	16!
	4!(16 - 4)!

Factorial Formula:

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

Calculate the numerator n!:

n! = 16!

16! = 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

16! = 20,922,789,888,000

Calculate (n - r)!:

(n - r)! = (16 - 4)!

(16 - 4)! = 12!

12! = 12 x 11 x 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1

12! = 479,001,600

Calculate r!:

r! = 4!

4! = 4 x 3 x 2 x 1

4! = 24

Calculate 16C4

16C4 =	20,922,789,888,000
	24 x 479,001,600

16C4 =	20,922,789,888,000
	11,496,038,400

16C4 = 1,820

Excel or Google Sheets formula:

=COMBIN(16,4)

What is the Answer?

16C4 = 1,820

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

16 Combinations of 4

Evaluate the combination: 16C4 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! = 16! 16! = 16 x 15 x 14 x 13 x 12 x 11 x 10