Imagine a fair lottery in which you choose six out of forty-nine numbers (1 through 49). Six numbers are drawn at random to determine a winner.

Consider the following two possible draws:

A: 1, 2, 3, 4, 5, 6

B: 5, 14, 19, 32, 44, 48

Which outcome, if any, is more likely?

In the context of a fair lottery where you choose six out of forty-nine numbers, the likelihood of any specific set of numbers being drawn is identical. 

### Key Points:

- **Total Number of Combinations:**
  - The total number of possible combinations of six numbers out of forty-nine can be calculated using the combination formula \( \binom{n}{k} \), where \( n \) is the total number of numbers (49 in this case), and \( k \) is the number of numbers chosen (6 here).
  - So, the total number of possible outcomes is:
    \[
    \binom{49}{6} = \frac{49!}{6!(49-6)!} = 13,983,816
    \]

- **Probability of Any Specific Outcome:**
  - Since there are \( 13,983,816 \) possible combinations, the probability of any specific combination (including both A: 1, 2, 3, 4, 5, 6 and B: 5, 14, 19, 32, 44, 48) being drawn is:
    \[
    \frac{1}{13,983,816}
    \]

### Conclusion:

Both outcomes A: 1, 2, 3, 4, 5, 6 and B: 5, 14, 19, 32, 44, 48 are **equally likely**. Each combination has the same probability of \( \frac{1}{13,983,816} \).

While outcome A might seem less random or more orderly, in terms of probability, there's no difference between it and any other combination. The lottery draw is a random process, and all combinations are equally likely to occur.

Would you like more details, or do you have any questions about the explanation?

### Related Questions:
1. What is the combination formula and how is it used in probability?
2. How do the odds of winning change with different lottery formats?
3. Why do people often believe certain number patterns are more likely than others?
4. How does the concept of randomness apply to lottery drawings?
5. Can understanding probability help in choosing lottery numbers?
6. What is the difference between combinations and permutations in probability?
7. How would the probability change if the lottery involved choosing more or fewer numbers?
8. How does the expectation value relate to playing the lottery?

**Tip:** In random processes, appearances can be deceiving—patterns or sequences that seem less random are just as likely as any other combination.

Explore the probability in fair lotteries by comparing the likelihood of two possible draws: A (1, 2, 3, 4, 5, 6) and B (5, 14, 19, 32, 44, 48). Learn about the total number of combinations, probability calculations, and why all outcomes are equally likely. Suitable for Grades 9-12.

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