39 Combinations of 6
Evaluate the combination:
39C6
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 = 39 and r = 6
39C6 2 | 39! |
6!(39 - 6)! |
Factorial Formula:
n! = n * (n - 1) * (n - 2) * .... * 2 * 1
Calculate the numerator n!:
n! = 39!
39! = 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
39! = 20,397,882,081,197,441,587,828,472,941,238,084,160,318,341,120
Calculate (n - r)!:
(n - r)! = (39 - 6)!
(39 - 6)! = 33!
33! = 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
33! = 8,683,317,618,811,885,938,715,673,895,318,323,200
Calculate r!:
r! = 6!
6! = 6 x 5 x 4 x 3 x 2 x 1
6! = 720
Calculate 39C6
39C6 = | 20,397,882,081,197,441,587,828,472,941,238,084,160,318,341,120 |
720 x 8,683,317,618,811,885,938,715,673,895,318,323,200 |
39C6 = | 20,397,882,081,197,441,587,828,472,941,238,084,160,318,341,120 |
6,251,988,685,544,558,234,775,137,902,722,228,944,896 |
39C6 = 3,262,623
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Excel or Google Sheets formula:
Excel or Google Sheets formula:=COMBIN(39,6)What is the Answer?
39C6 = 3,262,623
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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