23 Combinations of 3 ·

05 Jul 2024, 00:00

23 Combinations of 3 Image to Crop

Evaluate the combination:

23C3

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 = 23 and r = 3

23C3 2	23!
	3!(23 - 3)!

Factorial Formula:

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

Calculate the numerator n!:

n! = 23!

23! = 23 x 22 x 21 x 20 x 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

23! = 25,852,016,738,884,978,212,864

Calculate (n - r)!:

(n - r)! = (23 - 3)!

(23 - 3)! = 20!

20! = 20 x 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

20! = 2,432,902,008,176,640,000

Calculate r!:

r! = 3!

3! = 3 x 2 x 1

3! = 6

Calculate 23C3

23C3 =	25,852,016,738,884,978,212,864
	6 x 2,432,902,008,176,640,000

23C3 =	25,852,016,738,884,978,212,864
	14,597,412,049,059,840,000

23C3 = 1,771

You have 1 free calculations remaining

Excel or Google Sheets formula:

Excel or Google Sheets formula:=COMBIN(23,3)

What is the Answer?

23C3 = 1,771

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

23 Combinations of 3

Evaluate the combination: 23C3 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! = 23! 23! = 23 x 22 x 21 x 20 x 19 x 18 x 17