To win the jackpot, 3 different numbers are randomly selected from 1 to 40 and one number from 1 to 26. The order of the first 3 numbers does not matter.

What is the probability of winning the jackpot on one try?

Type your answer as a fraction or in scientific notation.


To calculate the probability of winning the jackpot, we need to determine the total number of possible outcomes and then find the probability of selecting the correct outcome.

### Step 1: Calculate the number of ways to choose 3 different numbers from 1 to 40
Since the order does not matter, we use the combination formula \( C(n, k) \):

\[
C(40, 3) = \frac{40!}{3!(40 - 3)!} = \frac{40!}{3! \times 37!}
\]

Calculating this:

\[
C(40, 3) = \frac{40 \times 39 \times 38}{3 \times 2 \times 1} = 9,880
\]

### Step 2: Calculate the number of ways to choose 1 number from 1 to 26
Since the order does not matter, and we are only choosing one number, the number of ways is simply 26.

### Step 3: Calculate the total number of possible outcomes
The total number of possible outcomes is the product of the two calculated numbers:

\[
\text{Total outcomes} = C(40, 3) \times 26 = 9,880 \times 26 = 256,880
\]

### Step 4: Calculate the probability of winning the jackpot
Since only one specific combination out of the total possible outcomes wins the jackpot, the probability of winning is:

\[
\text{Probability} = \frac{1}{256,880}
\]

Thus, the probability of winning the jackpot on one try is \( \frac{1}{256,880} \).

Would you like to dive into more details or have any questions?

Here are 5 related questions:
1. How does the probability change if you select 4 numbers instead of 3 from the 40?
2. What is the probability of winning if the numbers were chosen in a specific order?
3. How does the jackpot probability compare to rolling a specific outcome on a 6-sided die?
4. What if the number range changes from 1 to 50 instead of 1 to 40—what’s the new probability?
5. What are the odds of winning the jackpot twice in a row?

**Tip:** When calculating probabilities in combinatorics, always check whether order matters. This affects whether you use combinations or permutations.

To win the jackpot, 3 different numbers are randomly selected from 1 to 40 and one number from 1 to 26. The order of the first 3 numbers does not matter.

What is the probability of winning the jackpot on one try?

Type your answer as a fraction or in scientific notation.

This detailed guide walks you through calculating the probability of winning a jackpot where 3 different numbers are selected from 1 to 40 and one number from 1 to 26. Learn about combinations, the combination formula, and basic probability principles. Ideal for high school students (Grades 10-12).

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