Evaluate the combination:
60C2
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 = 60 and r = 2
| 60C2 2 | 60! |
| 2!(60 - 2)! |
Factorial Formula:
n! = n * (n - 1) * (n - 2) * .... * 2 * 1
Calculate the numerator n!:
n! = 60!
60! = 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
60! = 8,320,987,112,741,391,580,056,396,102,959,641,077,457,945,541,076,708,813,599,085,350,531,187,384,917,164,032
Calculate (n - r)!:
(n - r)! = (60 - 2)!
(60 - 2)! = 58!
58! = 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
58! = 2,350,561,331,282,878,906,297,796,280,456,247,634,956,966,273,955,390,268,712,005,058,924,708,557,225,984
Calculate r!:
r! = 2!
2! = 2 x 1
2! = 2
Calculate 60C2
| 60C2 = | 8,320,987,112,741,391,580,056,396,102,959,641,077,457,945,541,076,708,813,599,085,350,531,187,384,917,164,032 |
| 2 x 2,350,561,331,282,878,906,297,796,280,456,247,634,956,966,273,955,390,268,712,005,058,924,708,557,225,984 |
| 60C2 = | 8,320,987,112,741,391,580,056,396,102,959,641,077,457,945,541,076,708,813,599,085,350,531,187,384,917,164,032 |
| 4,701,122,662,565,757,812,595,592,560,912,495,269,913,932,547,910,780,537,424,010,117,849,417,114,451,968 |
60C2 = 1,770
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Excel or Google Sheets formula:
Excel or Google Sheets formula:=COMBIN(60,2)
What is the Answer?
60C2 = 1,770
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
