The Powerball lottery is decided every Monday, Wednesday and Saturday night by drawing
five white balls out of a drum with 69 balls and one red ball out of a drum with 26 red balls.
The Powerball jackpot is won by matching all five white balls in any order and the red Powerball. Each ticket costs $2. A ticket is defined as a set of five white and 1 red number.
How many possible different Powerball tickets can be purchased?

To calculate the total number of possible different Powerball tickets, we need to determine how many ways we can choose 5 white balls from a set of 69, and 1 red ball from a set of 26.

### Step 1: Calculating the combinations of white balls
The number of ways to choose 5 white balls from 69 is a combination problem. The formula for combinations is given by:

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

Where:
- $ n = 69 $ (total number of white balls),
- $ k = 5 $ (number of white balls chosen).

So, the number of ways to choose 5 white balls from 69 is:

\[
C(69, 5) = \frac{69!}{5!(69-5)!} = \frac{69!}{5!64!}
\]

### Step 2: Calculating the number of red balls
There are 26 red balls, and we choose 1. So, the number of ways to choose the red ball is simply 26.

### Step 3: Calculating the total number of different tickets
The total number of different tickets is the product of the number of ways to choose the white balls and the number of ways to choose the red ball:

\[
\text{Total tickets} = C(69, 5) \times 26
\]

Let's calculate this.

It seems like I can’t do more advanced data analysis right now. Please try again later. However, you can calculate the total number of Powerball tickets manually by following these steps:

1. Use the combination formula to find how many ways to choose 5 white balls from 69:
   \[
   C(69, 5) = \frac{69!}{5!(69-5)!} = \frac{69!}{5!64!}
   \]
2. Once you get the result, multiply it by 26 (the number of red balls).

Would you like more detailed help on how to manually calculate this? Feel free to ask questions!

Here are 5 related questions:
1. What is the probability of winning the Powerball jackpot?
2. How does the combination formula differ from permutations?
3. What is the probability of matching only the red ball?
4. How many ways can you choose any 5 numbers from a different total, such as 50?
5. What are the odds of matching 3 white balls and the red ball?

**Tip:** Using a scientific calculator or a tool like Python is handy for handling large combination calculations!

The Powerball lottery is decided every Monday, Wednesday and Saturday night by drawing five white balls out of a drum with 69 balls and one red ball out of a drum with 26 red balls. The Powerball jackpot is won by matching all five white balls in any order and the red Powerball. Each ticket costs $2. A ticket is defined as a set of five white and 1 red number. How many possible different Powerball tickets can be purchased?

Discover how to calculate the total number of possible Powerball ticket combinations using combinatorial mathematics. This problem involves choosing 5 white balls from 69 and 1 red ball from 26, demonstrating key concepts in combinatorics and probability. Suitable for high school students in Grades 10-12.

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