Associated Topics || Dr. Math Home || Search Dr. Math

### 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
are:

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
http://mathforum.org/dr.math/
```

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

Dear Dr. Math,

```
Associated Topics:
High School Probability

Search the Dr. Math Library:

 Find items containing (put spaces between keywords):   Click only once for faster results: [ Choose "whole words" when searching for a word like age.] all keywords, in any order at least one, that exact phrase parts of words whole words

Submit your own question to Dr. Math
Math Forum Home || Math Library || Quick Reference || Math Forum Search