Don't Play the Lottery

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Please, please Don't Play the Lottery. The odds are just so, so, so bad. Let's use combinatorics to see why.

The Rules of the PowerBall Lottery

A player will first select five numbers from $1$ to $69$. No repeats and order is not important.

How many distinct ways can a player do this? Because order is not important, we use combinations formula, where $n$ is $69$ and $r$ is $5$.

$$\frac{69!}{5!64!}$$

$11$,$238$,$513$

A player will then select a PowerBall number from $1$ to $26$. There are obviously only $26$ possibilities here.

Finding the Odds

A player must not only select the $5$ correct numbers from $1$ to $69$ but also separately select the correct PowerBall number from $1$ to $26$.

$11$,$238$,$513$$\times 26$

$292$,$201$,$338$

So, if you wanted to gaurantee that you'd win the lottery, you'd have to buy about $300$ million tickets. Don't play the lottery. 

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