58 Combinations of 6 ·

13 Jul 2024, 00:00

Evaluate the combination:

58C6

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 = 58 and r = 6

58C6 2	58!
	6!(58 - 6)!

Factorial Formula:

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

Calculate the numerator n!:

n! = 58!

58! = 58 x 57 x 56 x 55 x 54 x 53 x 52 x 51 x 50 x 49 x 48 x 47 x 46 x 45 x 44 x 43 x 42 x 41 x 40 x 39 x 38 x 37 x 36 x 35 x 34 x 33 x 32 x 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

58! = 2,350,561,331,282,878,906,297,796,280,456,247,634,956,966,273,955,390,268,712,005,058,924,708,557,225,984

Calculate (n - r)!:

(n - r)! = (58 - 6)!

(58 - 6)! = 52!

52! = 52 x 51 x 50 x 49 x 48 x 47 x 46 x 45 x 44 x 43 x 42 x 41 x 40 x 39 x 38 x 37 x 36 x 35 x 34 x 33 x 32 x 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

52! = 80,658,175,170,943,876,845,634,591,553,351,679,477,960,544,579,306,048,386,139,594,686,464

Calculate r!:

r! = 6!

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

6! = 720

Calculate 58C6

58C6 =	2,350,561,331,282,878,906,297,796,280,456,247,634,956,966,273,955,390,268,712,005,058,924,708,557,225,984
	720 x 80,658,175,170,943,876,845,634,591,553,351,679,477,960,544,579,306,048,386,139,594,686,464

58C6 =	2,350,561,331,282,878,906,297,796,280,456,247,634,956,966,273,955,390,268,712,005,058,924,708,557,225,984
	58,073,886,123,079,596,117,905,471,124,315,891,593,966,051,941,816,553,646,580,264,998,010,880

58C6 = 40,475,358

You have 1 free calculations remaining

Excel or Google Sheets formula:

Excel or Google Sheets formula:=COMBIN(58,6)

What is the Answer?

58C6 = 40,475,358

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

58 Combinations of 6

Evaluate the combination: 58C6 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! = 58! 58! = 58 x 57 x 56 x 55 x 54 x 53 x 52