In a certain lottery, five different numbers between 1 and 39 inclusive are drawn. These are the winning numbers. To win the lottery, a person must select the 5 correct numbers in the same order in which they were drawn. What is the possiblity of winning?
There are 39P5 ways to pick the numbers
Only one set wins, so
P(win) = 1/39P5
not very likely.
Lottery
To calculate the possibility of winning the lottery, we first need to determine the total number of possible outcomes or combinations.
In this case, we have five different numbers drawn from a range of 1 to 39 inclusive. Let's break down the process step by step:
Step 1: Find the number of possible choices for the first number. Since we have a range of 1 to 39 inclusive, there are 39 options.
Step 2: Once we have chosen the first number, we move on to the second number. Since the numbers need to be different, we now have 38 options for the second number.
Step 3: For the third number, we have 37 options left.
Step 4: For the fourth number, we have 36 options left.
Step 5: Finally, for the fifth and last number, there are 35 options.
To calculate the total number of combinations, we multiply the number of options for each step:
Total combinations = 39 options * 38 options * 37 options * 36 options * 35 options.
Now, let's calculate the number of possible combinations:
Total combinations = 575,757,600.
Therefore, there are a total of 575,757,600 different combinations in the lottery.
To determine the possibility of winning, we need to know the number of ways to win, which is just 1 (since there is only one winning combination).
The probability of winning is then calculated by dividing the number of ways to win by the total number of combinations:
Probability of winning = 1 / 575,757,600.
Hence, the possibility of winning this specific lottery is 1 in 575,757,600.