Evaluate the combination:
49C7
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 = 49 and r = 7
| 49C7 2 | 49! |
| 7!(49 - 7)! |
Factorial Formula:
n! = n * (n - 1) * (n - 2) * .... * 2 * 1
Calculate the numerator n!:
n! = 49!
49! = 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
49! = 608,281,864,034,267,522,488,601,608,116,731,623,168,777,542,102,418,391,010,639,872
Calculate (n - r)!:
(n - r)! = (49 - 7)!
(49 - 7)! = 42!
42! = 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
42! = 1,405,006,117,752,879,788,779,635,797,590,784,832,178,972,610,527,232
Calculate r!:
r! = 7!
7! = 7 x 6 x 5 x 4 x 3 x 2 x 1
7! = 5,040
Calculate 49C7
| 49C7 = | 608,281,864,034,267,522,488,601,608,116,731,623,168,777,542,102,418,391,010,639,872 |
| 5,040 x 1,405,006,117,752,879,788,779,635,797,590,784,832,178,972,610,527,232 |
| 49C7 = | 608,281,864,034,267,522,488,601,608,116,731,623,168,777,542,102,418,391,010,639,872 |
| 7,081,230,833,474,513,888,212,957,203,863,203,194,073,908,744,913,158,144 |
49C7 = 85,900,584
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Excel or Google Sheets formula:
Excel or Google Sheets formula:=COMBIN(49,7)What is the Answer?
49C7 = 85,900,584
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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