Many states use a lottery such as Powerball. Game tickets select 5 white balls numbered 1 to 69 and one red ball numbered from 1 to 26.
Suppose a person wanted to purchase a lottery ticket every minute, each one with a new combination of numbers. At that rate, how many days would it take to purchase all possible ticket combinations?
To calculate the number of days it would take to purchase all possible ticket combinations, we need to determine the total number of unique combinations.
Possible white ball combinations: 69 choose 5 (C(69,5))
Possible red ball combinations: 26
To calculate the total number of unique combinations, we multiply these two values:
Total combinations = C(69,5) * 26
Now, let's calculate the number of minutes it would take to purchase all possible ticket combinations if a person buys one ticket every minute:
Minutes = Total combinations / 1
To convert this into days, we divide the total number of minutes by the number of minutes in a day (24 * 60):
Days = Minutes / (24 * 60)
Let's calculate the number of days required.
To determine how many days it would take to purchase all possible ticket combinations, we need to calculate the total number of ticket combinations.
For the white balls, there are 69 possible numbers, and we need to select 5 of them without replacement (order doesn't matter). This can be calculated using the combination formula: C(n, r) = n! / (r! * (n-r)!), where n is the total number of items, and r is the number of items to be chosen at a time.
In this case, there are 69 white balls, and we need to select 5 of them. So, the number of possible combinations for the white balls is C(69, 5) = 11,238,513.
For the red ball, there are 26 possible numbers, and we need to select just 1. So, there are 26 possible combinations for the red ball.
To calculate the total number of ticket combinations, we multiply the number of combinations for the white balls by the number of combinations for the red ball:
Total combinations = 11,238,513 * 26 = 291,201,384.
Now that we know the total number of ticket combinations, we can calculate the number of minutes it would take to purchase all the tickets. Since the person wants to purchase a ticket every minute, we divide the total number of combinations by the number of tickets purchased per minute:
Total time in minutes = total combinations / tickets per minute = 291,201,384 / 1 = 291,201,384.
Assuming there are 60 minutes in an hour and 24 hours in a day, we can further calculate the number of days it would take:
Total time in days = total time in minutes / (minutes per hour * hours per day) = 291,201,384 / (60 * 24) = 201,669.
Therefore, at the rate of purchasing one ticket per minute, it would take approximately 201,669 days to purchase all possible ticket combinations.
There are 69P5 * 26 different tickets
There are 1440 minutes in a day
So divide.
It will take 2.4*10^7 days