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 matternPr = 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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