math-suite/Source/Help/documentation/apps/calculator/combinatorics.htm

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<title>Scientific Calculator: Combinatorics</title>
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<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>
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<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" />
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<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>
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<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" />
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<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" />
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