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Combinations - Winning at Powerball

In the multistate lottery game Powerball, there are 120,526,770 possible number combinations, only one of which is the grand prize winner. The cost of a single ticket (one number combination) is $1. Suppose that a very wealthy person decides to buy tickets for every possible number combination to be assured of winning a $150 million grand prize.

(a) If this individual could purchase one ticket every second, how many hours would it take to buy all of the tickets? How many years is this?

(b) If there were a way for this individual to buy all possible number combinations quickly, discuss reasons why this strategy would probably lose money.

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Solution Preview

There are 60 seconds in a minute and 60 minutes in an hour. So, there are 60 x 60 or 3600 seconds in an hour. To determine how many hours it would take to buy tickets for all possible combinations if we could buy one per second, we divide the total number of combinations by 3600. 120,526,770/3600 = number ...

Solution Summary

The solution has too parts. In the first part, we compute the number of possible Powerball tickets. In the second part, we consider whether or not purchasing all possible combinations of numbers, thus guaranteeing a winning ticket, would pay off.