48 Combinations of 3

Evaluate the combination:

48C3

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 = 48 and r = 3

48C3  2	48!
	3!(48 - 3)!

Factorial Formula:

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

Calculate the numerator n!:

n! = 48!

48! = 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

48! = 12,413,915,592,536,072,528,327,568,319,343,857,274,511,609,591,659,416,151,654,400

Calculate (n - r)!:

(n - r)! = (48 - 3)!

(48 - 3)! = 45!

45! = 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

45! = 119,622,220,865,480,188,574,992,723,157,469,373,503,186,265,858,579,103,744

Calculate r!:

r! = 3!

3! = 3 x 2 x 1

3! = 6

Calculate 48C3

48C3  =	12,413,915,592,536,072,528,327,568,319,343,857,274,511,609,591,659,416,151,654,400
	6 x 119,622,220,865,480,188,574,992,723,157,469,373,503,186,265,858,579,103,744

48C3  =	12,413,915,592,536,072,528,327,568,319,343,857,274,511,609,591,659,416,151,654,400
	717,733,325,192,881,087,893,813,373,064,692,917,707,167,843,885,143,556,096

48C3 = 17,296

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Excel or Google Sheets formula:

Excel or Google Sheets formula:=COMBIN(48,3)

What is the Answer?

48C3 = 17,296

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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Permutations and Combinations Calculator Video

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