In a lottery game, a player picks 6 numbers from 1 to 47. If 5 of the 6 numbers match those drawn, the player wins second prize. What is the probability of winning this prize? ***Be sure to leave your answer as a fraction in order to earn credit.***

There is a 24610737573​Incorrect probability of winning second prize.



*Hint:* The chances of winning are the total ways you can pick 5 out of 6 numbers divided by the number of ways you can pick 6 numbers out of 47.

To calculate the probability of winning second prize in the lottery, we need to determine two things:

1. The number of ways the player can match **5 out of the 6** numbers they chose.
2. The total number of ways **6 numbers** can be chosen out of the 47 possible numbers.

### Step 1: Total number of possible combinations
The total number of ways to choose 6 numbers out of 47 is calculated using the **combination formula**:

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

Where:
- \( n = 47 \) (total numbers available),
- \( k = 6 \) (numbers chosen).

This gives us the total number of ways to choose 6 numbers from 47.

### Step 2: Favorable outcomes (matching 5 of 6 numbers)
For the second prize, the player must match **5 out of the 6** chosen numbers. The player can:
- Choose 5 numbers from the 6 correct numbers, and
- Choose 1 number from the 41 remaining numbers (since 6 numbers are drawn, the remaining 41 numbers are incorrect).

So, we need to calculate:
- \( \binom{6}{5} \) for selecting 5 correct numbers,
- \( \binom{41}{1} \) for selecting 1 incorrect number.

### Step 3: Probability formula
The probability is given by:

\[
P(\text{second prize}) = \frac{\binom{6}{5} \times \binom{41}{1}}{\binom{47}{6}}
\]

Let me calculate this.It seems like I can’t do more advanced data analysis right now. Please try again later.

However, I can guide you on how to calculate the probability manually:

1. **Total combinations** of choosing 6 numbers from 47:
\[
\binom{47}{6} = \frac{47!}{6!(47-6)!}
\]

2. **Favorable outcomes**: Choose 5 correct numbers from 6 and 1 incorrect from 41:
\[
\binom{6}{5} \times \binom{41}{1}
\]

Finally, the probability is the ratio of favorable outcomes to total combinations:
\[
P = \frac{\binom{6}{5} \times \binom{41}{1}}{\binom{47}{6}}
\] 

Would you like any additional help with this?

In a lottery game, a player picks 6 numbers from 1 to 47. If 5 of the 6 numbers match those drawn, the player wins second prize. What is the probability of winning this prize? Be sure to leave your answer as a fraction in order to earn credit.

Discover how to calculate the probability of winning second prize in a lottery game by picking 6 numbers out of 47. This problem explores combinatorics and probability using the combination formula and covers key concepts suitable for students in Grades 10-12.

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