🎫 Lottery: 6 out of 49 – What are the chances of winning?
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Task:
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In classic lottery, 6 balls are drawn from 49. The question is: What is the probability of matching all 6 numbers?
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Step-by-step Solution:
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- Calculate combinations: Drawing 6 numbers from 49 is done without order and without replacement.
- Formula for combinations: \(C(n, k) = \frac{n!}{k! \cdot (n-k)!}\)
- Insert the numbers: \( C(49, 6) = \frac{49!}{6! \cdot 43!} = 13983816 \)
- Calculate probability: There is exactly 1 correct combination out of 13,983,816 possibilities.
- Result: Probability = \(\frac{1}{13\,983\,816}\) ≈ 0.0000000715
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Answer:
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The probability of getting a "six" in lottery is 1 in 13,983,816.
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