44 Combinations of 4 ·

11 Apr 2024, 00:00

Evaluate the combination:

44C4

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 = 44 and r = 4

44C4 2	44!
	4!(44 - 4)!

Factorial Formula:

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

Calculate the numerator n!:

n! = 44!

44! = 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

44! = 2,658,271,574,788,448,529,134,213,028,096,241,889,243,150,262,529,425,408

Calculate (n - r)!:

(n - r)! = (44 - 4)!

(44 - 4)! = 40!

40! = 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

40! = 815,915,283,247,897,683,795,548,521,301,193,790,359,984,930,816

Calculate r!:

r! = 4!

4! = 4 x 3 x 2 x 1

4! = 24

Calculate 44C4

44C4 =	2,658,271,574,788,448,529,134,213,028,096,241,889,243,150,262,529,425,408
	24 x 815,915,283,247,897,683,795,548,521,301,193,790,359,984,930,816

44C4 =	2,658,271,574,788,448,529,134,213,028,096,241,889,243,150,262,529,425,408
	19,581,966,797,949,544,411,093,164,511,228,650,968,639,638,339,584

44C4 = 135,751

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Excel or Google Sheets formula:

Excel or Google Sheets formula:=COMBIN(44,4)

What is the Answer?

44C4 = 135,751

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

44 Combinations of 4

Evaluate the combination: 44C4 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! = 44! 44! = 44 x 43 x 42 x 41 x 40 x 39 x 38