Evaluate the combination:
81C3
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 = 81 and r = 3
| 81C3 2 | 81! |
| 3!(81 - 3)! |
Factorial Formula:
n! = n * (n - 1) * (n - 2) * .... * 2 * 1
Calculate the numerator n!:
n! = 81!
81! = 81 x 80 x 79 x 78 x 77 x 76 x 75 x 74 x 73 x 72 x 71 x 70 x 69 x 68 x 67 x 66 x 65 x 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
81! = 5,797,126,020,747,365,547,859,207,609,316,955,153,302,418,317,114,924,299,299,934,140,244,381,749,043,408,420,663,995,193,999,459,259,329,102,516,576,025,837,568
Calculate (n - r)!:
(n - r)! = (81 - 3)!
(81 - 3)! = 78!
78! = 78 x 77 x 76 x 75 x 74 x 73 x 72 x 71 x 70 x 69 x 68 x 67 x 66 x 65 x 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
78! = 11,324,281,178,206,294,606,285,193,764,734,547,659,641,544,873,910,049,469,239,570,110,699,644,621,282,776,159,978,832,493,218,689,331,409,071,173,009,408
Calculate r!:
r! = 3!
3! = 3 x 2 x 1
3! = 6
Calculate 81C3
| 81C3 = | 5,797,126,020,747,365,547,859,207,609,316,955,153,302,418,317,114,924,299,299,934,140,244,381,749,043,408,420,663,995,193,999,459,259,329,102,516,576,025,837,568 |
| 6 x 11,324,281,178,206,294,606,285,193,764,734,547,659,641,544,873,910,049,469,239,570,110,699,644,621,282,776,159,978,832,493,218,689,331,409,071,173,009,408 |
| 81C3 = | 5,797,126,020,747,365,547,859,207,609,316,955,153,302,418,317,114,924,299,299,934,140,244,381,749,043,408,420,663,995,193,999,459,259,329,102,516,576,025,837,568 |
| 67,945,687,069,237,767,637,711,162,588,407,285,957,849,269,243,460,296,815,437,420,664,197,867,727,696,656,959,872,994,959,312,135,988,454,427,038,056,448 |
81C3 = 85,320
You have 1 free calculations remaining
Excel or Google Sheets formula:
Excel or Google Sheets formula:=COMBIN(81,3)
What is the Answer?
81C3 = 85,320
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?
- combination
- a 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)! - factorial
- The product of an integer and all the integers below it
- permutation
- a way in which a set or number of things can be ordered or arranged.
nPr = n!/(n - r)! - permutations and combinations
