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Ticket Lottery Puzzle - Spotify.html
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Ticket Lottery Puzzle - Spotify.html
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<!DOCTYPE html>
<!-- saved from url=(0093)http://web.archive.org/web/20120824220228/http://www.spotify.com/us/jobs/tech/ticket-lottery/ -->
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<title>Ticket Lottery Puzzle - Spotify</title>
<meta name="description" content="Spotify is a digital music service that gives you access to millions of songs.">
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<a href="http://web.archive.org/web/" title="Wayback Machine home page" style="background-color:transparent;border:none;"><img src="./Ticket Lottery Puzzle - Spotify_files/wayback-toolbar-logo.png" alt="Wayback Machine" width="110" height="39" border="0"></a>
</td>
<td style="padding:0!important;text-align:center;vertical-align:top;width:100%;">
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<a href="http://web.archive.org/web/20120629105811/http://www.spotify.com/us/jobs/tech/ticket-lottery/" style="text-decoration:none;color:#33f;font-weight:bold;background-color:transparent;border:none;" title="29 Jun 2012"><strong>JUN</strong></a>
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<td style="padding-left:9px;font-size:11px!important;font-weight:bold;text-transform:uppercase;white-space:nowrap;overflow:visible;" nowrap="nowrap">
<a href="http://web.archive.org/web/20121006093946/http://www.spotify.com/us/jobs/tech/ticket-lottery" style="text-decoration:none;color:#33f;font-weight:bold;background-color:transparent;border:none;" title="6 Oct 2012"><strong>OCT</strong></a>
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<a href="http://web.archive.org/web/20120806014055/http://www.spotify.com/us/jobs/tech/ticket-lottery/" title="1:40:55 Aug 6, 2012" style="background-color:transparent;border:none;"><img src="./Ticket Lottery Puzzle - Spotify_files/wm_tb_prv_on.png" alt="Previous capture" width="14" height="16" border="0"></a>
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<td style="padding-left:9px;white-space:nowrap;overflow:visible;text-align:left!important;vertical-align:middle!important;" nowrap="nowrap">
<a href="http://web.archive.org/web/20120903120703/http://www.spotify.com/us/jobs/tech/ticket-lottery/" title="12:07:03 Sep 3, 2012" style="background-color:transparent;border:none;"><img src="./Ticket Lottery Puzzle - Spotify_files/wm_tb_nxt_on.png" alt="Next capture" width="14" height="16" border="0"></a>
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<!-- NEXT/PREV YEAR NAV AND YEAR INDICATOR -->
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<a href="http://web.archive.org/web/20110812002443/http://www.spotify.com/us/jobs/tech/ticket-lottery/" style="text-decoration:none;color:#33f;font-weight:bold;background-color:transparent;border:none;" title="12 Aug 2011"><strong>2011</strong></a>
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<td style="padding-left:9px;font-size:11px!important;font-weight: bold;white-space:nowrap;overflow:visible;" nowrap="nowrap">
2013
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<td style="vertical-align:middle;padding:0!important;">
<a href="http://web.archive.org/web/20120824220228*/http://www.spotify.com/us/jobs/tech/ticket-lottery/" style="color:#33f;font-size:11px;font-weight:bold;background-color:transparent;border:none;" title="See a list of every capture for this URL"><strong>43 captures</strong></a>
<div class="__wb_banner_div" style="margin:0!important;padding:0!important;color:#666;font-size:9px;padding-top:2px!important;white-space:nowrap;" title="Timespan for captures of this URL">12 Aug 11 - 28 Jun 13</div>
</td>
<td style="padding:0!important;">
<a style="position:relative; white-space:nowrap; width:450px;height:27px;" href="http://web.archive.org/web/20070115000000/http://www.spotify.com/us/jobs/tech/ticket-lottery/" id="wm-graph-anchor">
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<div id="container">
<div id="header">
<a href="http://web.archive.org/web/20120824220228/http://www.spotify.com/us/" class="logo">Spotify</a>
<ul class="menu"><li><a href="http://web.archive.org/web/20120824220228/http://www.spotify.com/us/about/what/">What is Spotify?</a></li><li><a href="http://web.archive.org/web/20120824220228/http://www.spotify.com/us/get-spotify/overview/">Get Spotify</a></li><li><a href="http://web.archive.org/web/20120824220228/http://www.spotify.com/us/mobile/overview/">Mobile</a></li><li><a href="http://web.archive.org/web/20120824220228/http://community.spotify.com/">Community</a></li><li><a href="http://web.archive.org/web/20120824220228/http://www.spotify.com/us/about-us/contact/">About us</a></li><li class="selected"><a href="http://web.archive.org/web/20120824220228/http://www.spotify.com/us/jobs/">Jobs</a></li><li><a href="http://web.archive.org/web/20120824220228/http://www.spotify.com/us/help/overview/">Help</a></li></ul>
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<div class="account">
<a href="http://web.archive.org/web/20120824220228/https://www.spotify.com/us/login/?forward_url=%2Fus%2Fjobs%2Ftech%2Fticket-lottery%2F" id="accountbtn">Log in<span>.</span></a>
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<form action="http://web.archive.org/web/20120824220228/https://www.spotify.com/us/login/" method="post">
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<input type="hidden" name="utm-keywords" value="71ee4a8bae8c52fe327408ba2d02092d">
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</p>
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<input type="password" name="password" tabindex="2" id="login-password">
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<h1>Ticket Lottery</h1>
<h2>Problem ID: lottery</h2>
<p class="piccopy">
<img width="178" height="228" class="" alt="" src="./Ticket Lottery Puzzle - Spotify_files/puzzle-ticket-lottery-b.jpg"><br>Picture in Public Domain via Wikimedia Commons
</p>
<p>
You and your friends are in New York and are planning to go see a Broadway musical. Unfortunately, New York being New York, the tickets are just a tiny bit expensive. But one of the shows has a ticket lottery each night where impecunious people such as you have a chance to win the right to buy slightly less expensive tickets to good seats. The lottery operates as follows. First, everyone interested enters the lottery. Then, n lucky winners are drawn, and each of these is offered to buy up to t
tickets.<br> Given the number of people p in your group (all of which entered the lottery) and the total number of people m that entered the lottery, what is the probability that you will be able to get tickets for your entire group? Assume that the n lucky winners are chosen uniformly at random from the m people that entered the lottery, and that each person can win at most once.
</p>
<h4>Input</h4>
<p>The input consists of a single line containing four integers:</p>
<ul>
<li>1 ≤ m ≤ 1000: the total number of people who entered the lottery.</li>
<li>1 ≤ n ≤ m: the total number of winners drawn.</li>
<li>1 ≤ t ≤ 100: the number of tickets each winner is allowed to buy.</li>
<li>1 ≤ p ≤ m: the number of people in your group.</li>
</ul>
<h4>Output</h4>
<p>
Output a single line containing the probability that your entire group can get tickets to the show. This probability should be given with an absolute error of at most 10<sup style="height: 0; line-height: 1; vertical-align: baseline; _vertical-align: bottom; position: relative; bottom: 1ex; font-size: .8em;">−9</sup>.
</p>
<div class="inputoutput">
<div class="leftcol">
<div class="colhead">Sample input 1</div>
<div class="inptbox">100 10 2 1</div>
</div>
<div class="inpbtn"></div>
<div class="rightcol">
<div class="colhead">Sample output 1</div>
<div class="inptbox">0.1</div>
</div>
</div>
<div class="inputoutput">
<div class="leftcol">
<div class="colhead">Sample input 1</div>
<div class="inptbox">100 10 2 2</div>
</div>
<div class="inpbtn"></div>
<div class="rightcol">
<div class="colhead">Sample output 1</div>
<div class="inptbox">0.1909090909</div>
</div>
</div>
<div class="inputoutput">
<div class="leftcol">
<div class="colhead">Sample input 1</div>
<div class="inptbox">10 10 5 1</div>
</div>
<div class="inpbtn"></div>
<div class="rightcol">
<div class="colhead">Sample output 1</div>
<div class="inptbox">1.0000000000</div>
</div>
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<h3>Solved puzzles & got hired</h3>
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<img width="70" height="70" class="size-full alignleft" alt="" src="./Ticket Lottery Puzzle - Spotify_files/solved-elias.jpg"> <br>
<p>
<span class="highlight">Elias Freider</span><br>Software Engineer </p>
</div>
<div>
<img width="70" height="70" class="size-full alignleft" alt="" src="./Ticket Lottery Puzzle - Spotify_files/solved-jimmy.jpg"> <br>
<p>
<span class="highlight">Jimmy Mårdell</span><br>Software Engineer </p>
</div>
<div>
<img width="70" height="70" class="size-full alignleft" alt="" src="./Ticket Lottery Puzzle - Spotify_files/solved-par.jpg"> <br>
<p>
<span class="highlight">Pär Bohrarper</span><br>Software Engineer </p>
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<h3>Submit response</h3>
<p>To submit a solution to a problem, send an e-mail to</p>
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<p>Include your source code files as attachments and the problem id or problem name as subject. Within minutes you will get a reply indicating whether your source code solved the problem, and if it didn't, an indication of what was wrong. Your source code can be in C, C++, Java, or Python (version 2.6). Input is read from stdin.</p>
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