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This problem involves calculating the probability of selecting 5 numbers out of 50, which corresponds to a combination problem.

To solve it, we use the following:

1. **Total possible combinations**: Since we are selecting 5 numbers from 50, the total number of combinations is given by the combination formula:

\[
C(n, k) = \frac{n!}{k!(n-k)!}
\]

Where:
- \( n = 50 \) (total numbers),
- \( k = 5 \) (numbers to pick).

2. **Exact combination probability**: Since there is only 1 winning combination, the probability is:

\[
\text{Probability} = \frac{1}{C(50, 5)}
\]

Now, I'll calculate the exact probability for you.The total number of possible combinations of 5 numbers from 50 is \( 2,118,760 \).

Thus, the probability of picking the exact combination of the 5 winning numbers is:

\[
\text{Probability} = \frac{1}{2,118,760}
\]

This is the reduced fraction representing the probability.

Would you like further details or have any questions?

Here are some related questions you might want to explore:
1. How does the probability change if we pick 6 numbers instead of 5?
2. What if the range of numbers changes from 1 to 60? How would that affect the probability?
3. How can we calculate the probability of matching exactly 3 out of 5 numbers?
4. What is the difference between combinations and permutations in probability?
5. Can the result be expressed as a decimal, and how is that useful in real-life lottery contexts?

**Tip**: Combinatorics and probability are closely related. For problems like this, always remember that order does not matter when using combinations.

If a lottery consists of picking 5 numbers from 1 to 50, what is the probability that you pick the exact combination of the 5 winning numbers?

Learn how to calculate the probability of selecting the exact combination of 5 winning numbers from 50 in a lottery. This detailed solution uses combinatorics and probability theory, including the combination formula C(n, k) and basic probability rules. Suitable for students in Grades 9-12.

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