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To solve this problem, we need to calculate the odds of winning a "Pick 5" game in which players choose 5 numbers out of a possible 40, with the condition that there are three winning tickets in the drawing.

### Step-by-Step Solution

1. **Determine Total Possible Combinations:**
   The total number of ways to choose 5 numbers out of 40 can be calculated using the combination formula:
   \[
   C(n, r) = \frac{n!}{r!(n - r)!}
   \]
   Here, \( n = 40 \) and \( r = 5 \):
   \[
   C(40, 5) = \frac{40!}{5! \times (40 - 5)!} = \frac{40!}{5! \times 35!}
   \]
   Simplifying this calculation yields:
   \[
   C(40, 5) = 658,008
   \]

2. **Calculate Odds of Winning with 3 Winning Tickets:**
   Since there are three winning tickets, this triples the probability of winning, meaning the odds would be approximately 3 out of the total number of possible combinations.

3. **Odds Calculation:**
   Thus, the odds of winning are:
   \[
   3 : 658,008
   \]

### Answer
The correct answer is:
- **3:658,008**

Would you like more details on any steps or have further questions?

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Here are some related questions to deepen your understanding:

1. How would the odds change if there were 4 winning tickets instead of 3?
2. How does changing the total pool of numbers (e.g., choosing 5 out of 50) affect the odds?
3. How are odds different from probabilities in lottery games?
4. What is the difference between "odds" and "combinations"?
5. How can calculating combinations help in other probability scenarios?

**Tip:** Remember, odds reflect the ratio of successful outcomes to total possible outcomes, while probability is often expressed as a percentage or fraction of the total possibilities.

Suppose the Lottery Commission offers a Pick 5 game, where the players choose 5 out of 40 numbers. What would the odds of winning be if there are three winning tickets in this drawing?

Learn how to calculate the odds of winning a Pick 5 lottery game by choosing 5 out of 40 numbers with three winning tickets available. This detailed solution includes concepts of probability and combinations, using the combination formula for finding total possible outcomes. Suitable for students in Grades 10-12.

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