In a certain lottery, five different numbers between 1 and 31 inclusive are drawn. These are the winning numbers. To win the lottery, a person must select the correct 5 numbers in the same exact order in which they were drawn. What is the probability of winning?

To determine the probability of winning the lottery, we need to calculate the number of favorable outcomes (winning combinations) divided by the total number of possible outcomes.

In this case, the total number of possible outcomes is the number of different ways we can choose 5 numbers from the set of 1 to 31, without considering the order. We can calculate this using combinations. The formula for combinations is:

nCr = n! / r!(n-r)!

where n is the total number of items to choose from, and r is the number of items to choose.

Using this formula, we can calculate the total number of possible outcomes:

n = 31 (the range of numbers)
r = 5 (the number of numbers to choose)

31C5 = 31! / 5!(31-5)!
= 31! / 5!26!
= (31 * 30 * 29 * 28 * 27) / (5 * 4 * 3 * 2 * 1)
= 169,911

So, there are 169,911 total possible outcomes.

Now, let's calculate the number of favorable outcomes (winning combinations). Since the order matters in this case, we need to choose the 5 numbers in the specific order they were drawn. Since we are selecting 5 different numbers, the number of favorable outcomes is simply 1.

Therefore, the probability of winning the lottery is:

P(winning) = favorable outcomes / total outcomes
= 1 / 169,911
≈ 0.00000588 (or about 1 in 169,911)

So, the probability of winning is approximately 0.00000588 or about 1 in 169,911.

To calculate the probability of winning the lottery, we need to determine the number of possible outcomes and divide it by the total number of possible combinations.

The total number of possible outcomes is determined by the number of choices for each number in the winning combination. Since there are 31 numbers to choose from and we need to select 5 different numbers, we can calculate it as:

31 choices for the first number * 30 choices for the second number * 29 choices for the third number * 28 choices for the fourth number * 27 choices for the fifth number

Therefore, the total number of possible outcomes is:

31 * 30 * 29 * 28 * 27 = 24,883,200

Now, we need to find the number of ways to win the lottery, which is only one since there is only one specific order of winning numbers.

So, the probability of winning the lottery is calculated as:

Number of ways to win / Total number of possible outcomes

1 / 24,883,200

Therefore, the probability of winning the lottery is approximately 0.0000000402, or 1 in 24,883,200.

To get the first number right is 1 out of 31 choices.

For the second number, there are only 30 choices (five different numbers)...
So the probability of getting all five numbers right would be:
(1/31)(1/30)...(1/27).