Evaluate the combination:
64C3
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 = 64 and r = 3
| 64C3 2 | 64! |
| 3!(64 - 3)! |
Factorial Formula:
n! = n * (n - 1) * (n - 2) * .... * 2 * 1
Calculate the numerator n!:
n! = 64!
64! = 64 x 63 x 62 x 61 x 60 x 59 x 58 x 57 x 56 x 55 x 54 x 53 x 52 x 51 x 50 x 49 x 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
64! = 126,886,932,185,884,165,437,806,897,585,122,925,290,119,029,064,705,209,778,508,545,103,477,590,511,637,067,401,789,440
Calculate (n - r)!:
(n - r)! = (64 - 3)!
(64 - 3)! = 61!
61! = 61 x 60 x 59 x 58 x 57 x 56 x 55 x 54 x 53 x 52 x 51 x 50 x 49 x 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
61! = 507,580,213,877,224,835,833,540,161,373,088,490,724,281,389,843,871,724,559,898,414,118,829,028,410,677,788,672
Calculate r!:
r! = 3!
3! = 3 x 2 x 1
3! = 6
Calculate 64C3
| 64C3 = | 126,886,932,185,884,165,437,806,897,585,122,925,290,119,029,064,705,209,778,508,545,103,477,590,511,637,067,401,789,440 |
| 6 x 507,580,213,877,224,835,833,540,161,373,088,490,724,281,389,843,871,724,559,898,414,118,829,028,410,677,788,672 |
| 64C3 = | 126,886,932,185,884,165,437,806,897,585,122,925,290,119,029,064,705,209,778,508,545,103,477,590,511,637,067,401,789,440 |
| 3,045,481,283,263,349,015,001,240,968,238,530,944,345,688,339,063,230,347,359,390,484,712,974,170,464,066,732,032 |
64C3 = 41,664
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Excel or Google Sheets formula:
Excel or Google Sheets formula:=COMBIN(64,3)What is the Answer?
64C3 = 41,664
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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