ag-gipp/GoUldI

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data/mathoid/295.mml

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<math 
  xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="StartBinomialOrMatrix n Choose k EndBinomialOrMatrix equals StartFraction n factorial Over k factorial left-parenthesis n minus k right-parenthesis factorial EndFraction">
  <semantics>
    <mrow data-semantic-type="relseq" data-semantic-role="equality" data-semantic-id="24" data-semantic-children="5,23" data-semantic-content="8">
      <mrow class="MJX-TeXAtom-ORD">
        <mrow data-semantic-type="vector" data-semantic-role="binomial" data-semantic-id="5" data-semantic-children="3,4" data-semantic-content="0,6" data-semantic-parent="24">
          <mrow class="MJX-TeXAtom-OPEN">
            <mo maxsize="2.047em" minsize="2.047em" data-semantic-type="fence" data-semantic-role="open" data-semantic-id="0" data-semantic-parent="5">(</mo>
          </mrow>
          <mfrac linethickness="0">
            <mrow data-semantic-added="true" data-semantic-type="line" data-semantic-role="binomial" data-semantic-id="3" data-semantic-children="1" data-semantic-parent="5">
              <mi data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-id="1" data-semantic-parent="3">n</mi>
            </mrow>
            <mrow data-semantic-added="true" data-semantic-type="line" data-semantic-role="binomial" data-semantic-id="4" data-semantic-children="2" data-semantic-parent="5">
              <mi data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-id="2" data-semantic-parent="4">k</mi>
            </mrow>
          </mfrac>
          <mrow class="MJX-TeXAtom-CLOSE">
            <mo maxsize="2.047em" minsize="2.047em" data-semantic-type="fence" data-semantic-role="close" data-semantic-id="6" data-semantic-parent="5">)</mo>
          </mrow>
        </mrow>
      </mrow>
      <mo data-semantic-type="relation" data-semantic-role="equality" data-semantic-id="8" data-semantic-parent="24" data-semantic-operator="relseq,=">=</mo>
      <mrow class="MJX-TeXAtom-ORD">
        <mfrac data-semantic-type="fraction" data-semantic-role="division" data-semantic-id="23" data-semantic-children="11,22" data-semantic-parent="24">
          <mrow data-semantic-type="punctuated" data-semantic-role="endpunct" data-semantic-id="11" data-semantic-children="9,10" data-semantic-content="10" data-semantic-parent="23">
            <mi data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-id="9" data-semantic-parent="11">n</mi>
            <mo data-semantic-type="punctuation" data-semantic-role="unknown" data-semantic-id="10" data-semantic-parent="11" data-semantic-operator="punctuated">!</mo>
          </mrow>
          <mrow data-semantic-type="punctuated" data-semantic-role="sequence" data-semantic-id="22" data-semantic-children="12,13,21,19" data-semantic-content="13,19" data-semantic-parent="23">
            <mi data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-id="12" data-semantic-parent="22">k</mi>
            <mo data-semantic-type="punctuation" data-semantic-role="unknown" data-semantic-id="13" data-semantic-parent="22" data-semantic-operator="punctuated">!</mo>
            <mrow data-semantic-type="fenced" data-semantic-role="leftright" data-semantic-id="21" data-semantic-children="20" data-semantic-content="14,18" data-semantic-parent="22">
              <mo stretchy="false" data-semantic-type="fence" data-semantic-role="open" data-semantic-id="14" data-semantic-parent="21" data-semantic-operator="fenced">(</mo>
              <mrow data-semantic-type="infixop" data-semantic-role="subtraction" data-semantic-id="20" data-semantic-children="15,17" data-semantic-content="16" data-semantic-parent="21">
                <mi data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-id="15" data-semantic-parent="20">n</mi>
                <mo data-semantic-type="operator" data-semantic-role="subtraction" data-semantic-id="16" data-semantic-parent="20" data-semantic-operator="infixop,−">−
                  <!-- − -->
                </mo>
                <mi data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-id="17" data-semantic-parent="20">k</mi>
              </mrow>
              <mo stretchy="false" data-semantic-type="fence" data-semantic-role="close" data-semantic-id="18" data-semantic-parent="21" data-semantic-operator="fenced">)</mo>
            </mrow>
            <mo data-semantic-type="punctuation" data-semantic-role="unknown" data-semantic-id="19" data-semantic-parent="22" data-semantic-operator="punctuated">!</mo>
          </mrow>
        </mfrac>
      </mrow>
    </mrow>
    <annotation encoding="application/x-tex">{\binom {n}{k}}={\frac {n!}{k!(n-k)!}}</annotation>
  </semantics>
</math>