To find the probability of winning this lottery, we need to determine how many possible combinations of 5 numbers can be chosen from the set of numbers 1 to 46, and then find the probability of selecting the exact winning combination.

Step 1: Determine the total number of possible combinations

Since the order in which the numbers are selected does not matter (it's a combination, not a permutation), the total number of ways to choose 5 numbers from a set of 46 is given by the combination formula:

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

Where:

• $n = 46$ (the total number of numbers available),
• $k = 5$ (the number of numbers chosen).

So we calculate:

$C(46, 5) = \frac{46!}{5!(46-5)!} = \frac{46 \times 45 \times 44 \times 43 \times 42}{5 \times 4 \times 3 \times 2 \times 1}$

$C(46, 5) = 1,221,759$

Step 2: Find the probability of winning

To win the lottery, the person must choose the exact combination of 5 numbers that are drawn. Since there is only 1 winning combination out of all 1,221,759 possible combinations, the probability $P$ of winning is:

$P = \frac{1}{1,221,759}$

So, the probability of winning is:

$P \approx 0.000000818$

Final Answer:

The probability that a person who buys one lottery ticket will win is approximately 1 in 1,221,759, or about 0.000000818.

Would you like more details or explanations?

Here are some related questions to explore further:

1. How would the probability change if more numbers were selected?
2. What is the difference between a combination and a permutation in lottery problems?
3. How can you calculate the odds of winning a lottery with different prize structures?
4. How do you calculate the probability of winning in a lottery with multiple draws?
5. How does the probability of winning change if the number range was increased to 50 or 60?

Tip: Always make sure to distinguish between combinations (where order doesn’t matter) and permutations (where order matters) when working with lottery-type problems.