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      <text>37.1.1.7 Combinations</text>
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      <text><![CDATA[<p>A <span><strong>combination</strong></span> of objects takes <span><strong>no account of order</strong></span> whereas a permutation does. The formula <span class="math inline">\(^nP_r=\dfrac{n!}{(n-r)!}\)</span> gives us the number of ordered sets of <span class="math inline">\(r\)</span> objects chosen from <span class="math inline">\(n\)</span>. Suppose the number of sets of <span class="math inline">\(r\)</span> objects (taken from <span class="math inline">\(n\)</span> objects) in which order is not taken into account is <span class="math inline">\(C\)</span>. It follows that
<br>\(\qquad C\times r!=\dfrac{n!}{(n-r)!}\)<br>
and so <span class="math inline">\(C\)</span> is given by the formula <br>\(\qquad C=\dfrac{n!}{r!(n-r)!}\)<br>
We normally denote the right-hand side of this expression by <span class="math inline">\(^nC_r\)</span> so that 
<br><span class="math inline">\(\qquad ^nC_r=\dfrac{n!}{r!(n-r)!}\)</span><br>A common alternative notation for <span class="math inline">\(^nC_r\)</span> is <span class="math inline">\(\left(\begin{matrix}n\\r\end{matrix}\right)\)</span>.</p>]]></text>
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