8 Combinations of 5 · - The Daily Insight

07 Jan 2024, 00:00

Evaluate the combination:

8C5

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 = 8 and r = 5

8C5 2	8!
	5!(8 - 5)!

Factorial Formula:

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

Calculate the numerator n!:

n! = 8!

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

8! = 40,320

Calculate (n - r)!:

(n - r)! = (8 - 5)!

(8 - 5)! = 3!

3! = 3 x 2 x 1

3! = 6

Calculate r!:

r! = 5!

5! = 5 x 4 x 3 x 2 x 1

5! = 120

Calculate 8C5

8C5 =	40,320
	120 x 6

8C5 =	40,320
	720

8C5 = 56

Excel or Google Sheets formula:

=COMBIN(8,5)

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