38 Combinations of 6 ·

30 Jun 2024, 00:00

Evaluate the combination:

38C6

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 = 38 and r = 6

38C6 2	38!
	6!(38 - 6)!

Factorial Formula:

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

Calculate the numerator n!:

n! = 38!

38! = 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

38! = 523,022,617,466,601,037,913,697,377,988,137,380,787,257,344

Calculate (n - r)!:

(n - r)! = (38 - 6)!

(38 - 6)! = 32!

32! = 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

32! = 263,130,836,933,693,517,766,352,317,727,113,216

Calculate r!:

r! = 6!

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

6! = 720

Calculate 38C6

38C6 =	523,022,617,466,601,037,913,697,377,988,137,380,787,257,344
	720 x 263,130,836,933,693,517,766,352,317,727,113,216

38C6 =	523,022,617,466,601,037,913,697,377,988,137,380,787,257,344
	189,454,202,592,259,320,985,857,461,589,408,481,280

38C6 = 2,760,681

Excel or Google Sheets formula:

=COMBIN(38,6)

What is the Answer?

38C6 = 2,760,681

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

38 Combinations of 6

Evaluate the combination: 38C6 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! = 38! 38! = 38 x 37 x 36 x 35 x 34 x 33 x 32