Combinations and permutations calculator
Order matters for permutations and does not for combinations. Both are computed exactly here.
Combinations, nCr
13 983 816
- Permutations, nPr
- 10 068 347 520
- Combinations with repetition
- 25 827 165
- Permutations with repetition
- 13 841 287 201
- Chance of one specific combination
- 7.1511238e-8
Show the working
- n (items to choose from) = 49
- r (items chosen) = 6
- Combinations, nCr = comb(49, 6) = 13 983 800
- Permutations, nPr = perm(49, 6) = 10 068 300 000
- Combinations with repetition = comb(49 + 6 - 1, 6) = 25 827 200
- Permutations with repetition = 49^6 = 13 841 300 000
- Chance of one specific combination = 13 983 800 > 0 ? 1/13 983 800 : 0 = 7.15112e-8
Values are shown to six significant figures here; the arithmetic itself runs on exact fractions and is only rounded where a number is printed.
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The formula
- nCr = n! / (r! (n-r)!)
- nPr = n! / (n-r)!
- with repetition: combinations = (n+r-1)Cr, permutations = n^r
49 choose 6 is 13 983 816, which is why a six-from-49 lottery ticket has those odds.