Evaluate the combination:
49C5
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 = 5
| 49C5 2 | 49! |
| 5!(49 - 5)! |
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 - 5)!
(49 - 5)! = 44!
44! = 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
44! = 2,658,271,574,788,448,529,134,213,028,096,241,889,243,150,262,529,425,408
Calculate r!:
r! = 5!
5! = 5 x 4 x 3 x 2 x 1
5! = 120
Calculate 49C5
| 49C5 = | 608,281,864,034,267,522,488,601,608,116,731,623,168,777,542,102,418,391,010,639,872 |
| 120 x 2,658,271,574,788,448,529,134,213,028,096,241,889,243,150,262,529,425,408 |
| 49C5 = | 608,281,864,034,267,522,488,601,608,116,731,623,168,777,542,102,418,391,010,639,872 |
| 318,992,588,974,613,807,162,551,951,166,502,780,467,196,874,778,656,899,072 |
49C5 = 1,906,884
You have 1 free calculations remaining
Excel or Google Sheets formula:
Excel or Google Sheets formula:=COMBIN(49,5)
What is the Answer?
49C5 = 1,906,884
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
