90 lines
2.9 KiB
HTML
90 lines
2.9 KiB
HTML
<!-- saved from url=(0014)about:internet -->
|
|
<html>
|
|
<meta http-equiv="X-UA-Compatible" content="IE=9" />
|
|
<head>
|
|
<title>Scientific Calculator: Combinatorics</title>
|
|
<link href="style.css" rel="stylesheet" type="text/css" />
|
|
|
|
</head>
|
|
|
|
<body>
|
|
<h1>Scientific Calculator: Combinatorics</h1>
|
|
|
|
<div class="section">
|
|
<h2>Content</h2>
|
|
<ul>
|
|
<li><a href="#fact">Factorial</a></li>
|
|
<li><a href="#perm">Permutations</a></li>
|
|
<li><a href="#permk">Permutations of k objects</a></li>
|
|
<li><a href="#comb">Combinations</a></li>
|
|
|
|
</ul>
|
|
</div>
|
|
|
|
|
|
<div class="section">
|
|
<a name="fact"></a>
|
|
<h2>Factorial</h2>
|
|
|
|
<p>In mathematics, the <em>factorial</em> of a natural number, denoted by <strong>n!</strong>, is the <em>product of all natural numbers smaller or equal to <strong>n</strong></em>.</p>
|
|
|
|
<img class="maths" src="img/calc-combinatorics-eq0.gif" />
|
|
|
|
<p>This can also be written as:</p>
|
|
<img class="maths" src="img/calc-combinatorics-eq1.gif" />
|
|
|
|
<p>By convention, <strong>0! = 1</strong>.</p>
|
|
<p>Example:</p>
|
|
<img class="maths" src="img/calc-combinatorics-eq2.gif" />
|
|
<br /> <br />
|
|
</div>
|
|
|
|
<div class="section">
|
|
<a name="perm"></a>
|
|
<h2>Permutations</h2>
|
|
|
|
<p>In mathematics, a <em>permutation</em> of a set of objects is defined as <em>a particular order</em> of the items.</p>
|
|
<p>For example, the permutations of the set <strong>{1, 2, 3}</strong> are:<br /> (1, 2, 3); (1, 3, 2); (2, 1, 3); (2, 3, 1); (3, 1, 2); (3, 2, 1);</p>
|
|
|
|
<p>The number of permutations for a set is given by <strong>n!</strong>.</p>
|
|
<br />
|
|
</div>
|
|
|
|
<div class="section">
|
|
<a name="permk"></a>
|
|
<h2>Permutations of k objects</h2>
|
|
|
|
<p>Example: the permutations of 2 items from the set <strong>{1, 2, 3}</strong> are:<br />
|
|
(1, 2); (2, 1); (1, 3); (3, 1); (2, 3); (3, 2); </p>
|
|
|
|
<p>The number of permutations of k objects is given by the formula:</p>
|
|
<img class="maths" src="img/calc-combinatorics-eq5.gif" />
|
|
<p> After making the simplifications, we get:</p>
|
|
<img class="maths" src="img/calc-combinatorics-eq6.gif" />
|
|
<br /> <br />
|
|
</div>
|
|
|
|
<div class="section">
|
|
<a name="comb"></a>
|
|
<h2>Combinations</h2>
|
|
|
|
<p>In mathematics, a <em>combination</em> is a method of selecting a number of objects from a larger set, where order doesn't matter.</p>
|
|
|
|
<p>For example, the combinations of 2 items from the set <strong>{1, 2, 3}</strong> are:<br />
|
|
{1, 2}; {1, 3}; {2, 3}; </p>
|
|
|
|
<p> The number of combinations is given by the formula:</p>
|
|
<img class="maths" src="img/calc-combinatorics-eq3.gif" />
|
|
<p> After making the simplifications, we get:</p>
|
|
<img class="maths" src="img/calc-combinatorics-eq4.gif" />
|
|
<br /><br />
|
|
</div>
|
|
|
|
|
|
|
|
<div class="footer">
|
|
Software created by Chibici Tiberiu.
|
|
Contact: <a href="mailto:chibicitiberiu@gmail.com">chibicitiberiu@gmail.com</a>
|
|
</div>
|
|
</body>
|
|
</html> |