Mega-Sena
- Input
- C(60, 6)
- Expected output
- 50063860
Formula C(60,6) = 60!/(6!×54!): 50,063,860 combinations, the odds for a single simple entry.
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combinations in lottery and probability
In Mega-Sena, you pick 6 numbers out of 60. C(60,6) = 50,063,860 possible combinations, so the odds of matching all 6 numbers with a single simple entry are about 1 in 50 million.
Formula C(60,6) = 60!/(6!×54!): 50,063,860 combinations, the odds for a single simple entry.
A smaller pool (25) but r close to half of it (15): still over 3 million possible combinations.
A larger pool (80) than Mega-Sena, but only 5 numbers drawn: the result lands between Lotofácil and Mega-Sena.
A combination is a selection of r elements from a set of n where the order of the chosen elements does not matter. For example, choosing 2 fruits from {apple, pear, grape} gives 3 combinations: {apple, pear}, {apple, grape}, and {pear, grape}. The count is given by C(n, r) = n! / (r! · (n − r)!).
Because the order of the draw does not matter: drawing 5-12-23-34-45-59 pays the same prize as drawing 59-45-34-23-12-5. A combination counts each group of numbers once; a permutation would count the same 6 numbers in up to 720 (6!) different orders, badly overestimating the total.
Because the calculation uses BigInt internally and the value is shown as is, without thousands formatting. 50063860 and 50,063,860 are the same number: the separator is just a reading convention, not part of the raw result.
Smaller: 24,040,016 versus 50,063,860. Even with a larger pool (80 versus 60), drawing only 5 numbers instead of 6 matters more in the count, because C(n,r) grows with r just as much as it grows with n.
C(n, r) = n! / (r! × (n−r)!)
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