Don't Play the Lottery

<p><a href="https://www.prepswift.com/quizzes/quiz/prepswift-dont-play-the-lottery" target="_blank">Don&#39;t Play the Lottery Exercise</a></p><p>Please, please <strong><span style="color:#8e44ad;">Don&#39;t Play the Lottery</span></strong>. The odds are just so, so, so bad. Let&#39;s use combinatorics to see why.</p> <p><strong><span style="color:#e74c3c;">The Rules of the PowerBall Lottery</span></strong></p> <p>A player will first select five numbers from $1$ to $69$. No repeats and order is not important.</p> <p style="margin-left: 40px;">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 $5$.</p> <p>$$\frac{69!}{5!64!}$$</p> <p style="text-align: center;">$11$,$238$,$513$</p> <p>A player will then select a PowerBall number from $1$ to $26$. There are obviously only $26$ possibilities here.</p> <p><strong><span style="color:#27ae60;">Finding the Odds</span></strong></p> <p>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 $26$.</p> <p style="text-align: center;">$11$,$238$,$513$$\times 26$</p> <p style="text-align: center;"><strong><span style="color:#e74c3c;"><span style="font-size:18px;">$292$,$201$,$338$</span></span></strong></p> <p>So, if you wanted to gaurantee that you&#39;d win the lottery, you&#39;d have to buy about $300$ million tickets. Don&#39;t play the lottery.&nbsp;</p>