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In this lottery game, 50 numbered ping-pong balls are available, and 5 are selected randomly. We are asked to find two things:

1. **Number of outcomes for picking 5 different numbers from the 50 balls**.
2. **Probability of picking the correct 5 numbers**.

### 1. Number of Outcomes
The number of ways to select 5 balls out of 50 is given by the combination formula:
\[
\binom{n}{r} = \frac{n!}{r!(n - r)!}
\]
Where:
- \( n = 50 \) (total number of balls),
- \( r = 5 \) (balls to be selected).

Substituting these values:
\[
\binom{50}{5} = \frac{50!}{5!(50 - 5)!} = \frac{50!}{5!45!}
\]

Calculating this (you can use a calculator or software):
\[
\binom{50}{5} = 2,118,760
\]

Thus, there are **2,118,760** possible ways to pick 5 numbers from 50.

### 2. Probability of Picking the Correct Numbers
The probability of picking the exact 5 correct numbers is:
\[
P = \frac{1}{\binom{50}{5}} = \frac{1}{2,118,760}
\]

So, the probability of winning the jackpot by picking the correct 5 numbers is approximately **1 in 2,118,760**.

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Would you like further details or have any questions?

Here are 5 related questions for further exploration:
1. How does the probability change if the total number of balls increases to 60?
2. What if the order in which the numbers are selected matters?
3. How does the probability compare to lotteries with fewer numbers, like selecting 5 out of 40?
4. What is the probability of matching exactly 4 out of the 5 chosen numbers?
5. How would the odds change if you were allowed to choose 6 numbers instead of 5?

**Tip**: When solving combinatorics problems, always carefully distinguish between cases where order matters (permutations) and cases where it doesn’t (combinations).

In a lottery game, 50 numbered ping-pong balls are put in a bin, and 5 are randomly chosen. To win the jackpot, you need to match all 5 numbers. Determine the number of outcomes for picking 5 different numbers from the 50 ping-pong balls and the probability of you picking the correct numbers.

In this lottery problem, learn how to calculate the number of possible outcomes and the probability of winning by picking 5 numbers from 50. Explore the combination formula and understand the odds with detailed steps. Suitable for high school students (Grades 9-12).

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