41 Combinations of 5

Evaluate the combination:

41C5

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 = 41 and r = 5

41C5 2	41!
	5!(41 - 5)!

Factorial Formula:

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

Calculate the numerator n!:

n! = 41!

41! = 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

41! = 33,452,526,613,163,802,763,987,613,764,361,857,922,667,238,129,664

Calculate (n - r)!:

(n - r)! = (41 - 5)!

(41 - 5)! = 36!

36! = 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

36! = 371,993,326,789,901,177,492,420,297,158,468,206,329,856

Calculate r!:

r! = 5!

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

5! = 120

Calculate 41C5

41C5 =	33,452,526,613,163,802,763,987,613,764,361,857,922,667,238,129,664
	120 x 371,993,326,789,901,177,492,420,297,158,468,206,329,856

41C5 =	33,452,526,613,163,802,763,987,613,764,361,857,922,667,238,129,664
	44,639,199,214,788,140,061,150,396,373,635,909,860,458,496

41C5 = 749,398

Excel or Google Sheets formula:

=COMBIN(41,5)

What is the Answer?

41C5 = 749,398

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

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