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Odds of Winning the PowerBall Lottery

Date: 08/29/2001 at 17:16:39
From: Joseph Flowers
Subject: Odds of winning the lottery

Dear Dr. Math,

A friend of mine says that a recently published article in the 
Louisville Courier Journal stating that the odds of winning the 
300-million-dollar powerball were just one in 80,089,128 is wrong.
He is a math teacher, but has yet to offer his odds on winning. 

Can you verify the paper's numbers?

Date: 08/29/2001 at 17:49:18
From: Doctor Paul
Subject: Re: Odds of winning the lottery

The newspaper is correct:

There are C(49,5) ways to choose the first five balls and clearly 
there are 42 ways to choose the powerball.  So the odds of winning 

C(49,5) * 42 = 

49!/(5! * (49-5)!) * 42 = 

42*45*46*47*48*49/120 = 80,089,128

So there are 80089128 possible ways to pick the lottery numbers and 
there is only one way to win (getting them all correct).  Hence the 
odds are 1:80089128.

- Doctor Paul, The Math Forum

Date: 08/30/2001 at 22:20:17
From: Joseph W. Flowers
Subject: Re: Odds of winning the lottery

Dear Dr. Math,

Thanks for your reply, and your answer so soon!
Associated Topics:
High School Probability

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