90 lines
2.9 KiB
HTML
90 lines
2.9 KiB
HTML
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<!-- saved from url=(0014)about:internet -->
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<html>
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<meta http-equiv="X-UA-Compatible" content="IE=9" />
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<head>
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<title>Scientific Calculator: Combinatorics</title>
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<link href="style.css" rel="stylesheet" type="text/css" />
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</head>
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<body>
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<h1>Scientific Calculator: Combinatorics</h1>
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<div class="section">
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<h2>Content</h2>
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<ul>
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<li><a href="#fact">Factorial</a></li>
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<li><a href="#perm">Permutations</a></li>
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<li><a href="#permk">Permutations of k objects</a></li>
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<li><a href="#comb">Combinations</a></li>
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</ul>
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</div>
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<div class="section">
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<a name="fact"></a>
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<h2>Factorial</h2>
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<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>
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<img class="maths" src="img/calc-combinatorics-eq0.gif" />
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<p>This can also be written as:</p>
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<img class="maths" src="img/calc-combinatorics-eq1.gif" />
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<p>By convention, <strong>0! = 1</strong>.</p>
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<p>Example:</p>
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<img class="maths" src="img/calc-combinatorics-eq2.gif" />
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<br /> <br />
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</div>
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<div class="section">
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<a name="perm"></a>
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<h2>Permutations</h2>
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<p>In mathematics, a <em>permutation</em> of a set of objects is defined as <em>a particular order</em> of the items.</p>
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<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>
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<p>The number of permutations for a set is given by <strong>n!</strong>.</p>
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<br />
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</div>
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<div class="section">
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<a name="permk"></a>
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<h2>Permutations of k objects</h2>
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<p>Example: the permutations of 2 items from the set <strong>{1, 2, 3}</strong> are:<br />
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(1, 2); (2, 1); (1, 3); (3, 1); (2, 3); (3, 2); </p>
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<p>The number of permutations of k objects is given by the formula:</p>
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<img class="maths" src="img/calc-combinatorics-eq5.gif" />
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<p> After making the simplifications, we get:</p>
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<img class="maths" src="img/calc-combinatorics-eq6.gif" />
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<br /> <br />
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</div>
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<div class="section">
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<a name="comb"></a>
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<h2>Combinations</h2>
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<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>
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<p>For example, the combinations of 2 items from the set <strong>{1, 2, 3}</strong> are:<br />
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{1, 2}; {1, 3}; {2, 3}; </p>
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<p> The number of combinations is given by the formula:</p>
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<img class="maths" src="img/calc-combinatorics-eq3.gif" />
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<p> After making the simplifications, we get:</p>
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<img class="maths" src="img/calc-combinatorics-eq4.gif" />
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<br /><br />
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</div>
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<div class="footer">
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Software created by Chibici Tiberiu.
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Contact: <a href="mailto:chibicitiberiu@gmail.com">chibicitiberiu@gmail.com</a>
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</div>
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</body>
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</html>
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