31 Combinations of 5 ·

30 Jun 2024, 00:00

Evaluate the combination:

31C5

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 = 31 and r = 5

31C5 2	31!
	5!(31 - 5)!

Factorial Formula:

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

Calculate the numerator n!:

n! = 31!

31! = 31 x 30 x 29 x 28 x 27 x 26 x 25 x 24 x 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

31! = 8,222,838,654,177,922,430,198,509,928,972,288

Calculate (n - r)!:

(n - r)! = (31 - 5)!

(31 - 5)! = 26!

26! = 26 x 25 x 24 x 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

26! = 403,291,461,126,605,650,322,784,256

Calculate r!:

r! = 5!

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

5! = 120

Calculate 31C5

31C5 =	8,222,838,654,177,922,430,198,509,928,972,288
	120 x 403,291,461,126,605,650,322,784,256

31C5 =	8,222,838,654,177,922,430,198,509,928,972,288
	48,394,975,335,192,675,289,955,041,280

31C5 = 169,911

You have 1 free calculations remaining

Excel or Google Sheets formula:

Excel or Google Sheets formula:=COMBIN(31,5)

What is the Answer?

31C5 = 169,911

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

31 Combinations of 5

Evaluate the combination: 31C5 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! = 31! 31! = 31 x 30 x 29 x 28 x 27 x 26 x 25