combinations in lottery and probability

Lottery Combinations — Real Probability

In Mega-Sena, you choose 6 from 60 numbers. C(60,6) = 50,063,860 — your odds of matching all six are 1 in ~50 million.

C(n, r) = n! / (r! × (n−r)!)

n (total elements)

r (elements chosen)

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Combinations and lottery probability

The probability of an event is (favorable outcomes) / (total outcomes). With one Mega-Sena ticket: P = 1/C(60,6) ≈ 2×10⁻⁸.
Combinations grow very fast with n and r. C(60,6) ≈ 5×10⁷. C(100,50) ≈ 10²⁹. Large values require BigInt for exact precision.

Examples

Mega-Sena

Input: C(60, 6)
Expected output: 50.063.860

Possible Mega-Sena combinations.

Lotofácil

Input: C(25, 15)
Expected output: 3.268.760

Possible Lotofácil combinations.

Full tool FAQ

What is a combination?

A combination is a selection of r elements from a set of n, where the order of selected elements does not matter. For example, choosing 2 fruits from {apple, pear, grape} gives 3 combinations: {apple, pear}, {apple, grape}, {pear, grape}.

What is the difference between combination and permutation?

What is a combination with repetition?

Why does C(n, 0) = 1?

Is C(n, r) = C(n, n-r)?

What is the maximum value of n and r?

What happens when the result exceeds 10¹⁰⁰?

What are the practical uses of combinations?

Frequently asked questions

Combination vs permutation in lotteries

In lotteries, order does not matter (numbers are drawn, not ranked). That is why we use combinations, not permutations.

Does this page replace official or professional review?

No. It helps explain the scenario and use the tool more safely, but real decisions should consider official sources, full context and qualified guidance when needed.