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mathmlben

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Visualization for goldstandard

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<math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="StartAbsoluteValue left-bracket k right-bracket Superscript n Baseline left-parenthesis 1 hyphen 1 right-parenthesis EndAbsoluteValue equals StartBinomialOrMatrix k Choose n EndBinomialOrMatrix n factorial equals left-parenthesis k right-parenthesis Subscript n Baseline"> <semantics> <mrow data-semantic-type="punctuated" data-semantic-role="sequence" data-semantic-id="43" data-semantic-children="40,22,42" data-semantic-content="22"> <mrow data-semantic-type="relseq" data-semantic-role="equality" data-semantic-id="40" data-semantic-children="36,39" data-semantic-content="12" data-semantic-parent="43"> <mrow data-semantic-type="fenced" data-semantic-role="neutral" data-semantic-id="36" data-semantic-children="35" data-semantic-content="0,11" data-semantic-parent="40"> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false" data-semantic-type="fence" data-semantic-role="neutral" data-semantic-id="0" data-semantic-parent="36" data-semantic-operator="fenced">|</mo> </mrow> <mrow data-semantic-type="infixop" data-semantic-role="implicit" data-semantic-id="35" data-semantic-children="5,33" data-semantic-content="34" data-semantic-parent="36"> <msup data-semantic-type="superscript" data-semantic-role="leftright" data-semantic-id="5" data-semantic-children="29,4" data-semantic-parent="35" data-semantic-fencepointer="3"> <mrow data-semantic-type="fenced" data-semantic-role="leftright" data-semantic-id="29" data-semantic-children="2" data-semantic-content="1,3" data-semantic-parent="5"> <mo stretchy="false" data-semantic-type="fence" data-semantic-role="open" data-semantic-id="1" data-semantic-parent="29">[</mo> <mi data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-id="2" data-semantic-parent="29">k</mi> <mo stretchy="false" data-semantic-type="fence" data-semantic-role="close" data-semantic-id="3" data-semantic-parent="29">]</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-id="4" data-semantic-parent="5">n</mi> </mrow> </msup> <mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-id="34" data-semantic-parent="35" data-semantic-added="true" data-semantic-operator="infixop,⁢"></mo> <mrow data-semantic-type="fenced" data-semantic-role="leftright" data-semantic-id="33" data-semantic-children="32" data-semantic-content="6,10" data-semantic-parent="35"> <mo stretchy="false" data-semantic-type="fence" data-semantic-role="open" data-semantic-id="6" data-semantic-parent="33" data-semantic-operator="fenced">(</mo> <mrow data-semantic-type="punctuated" data-semantic-role="text" data-semantic-id="32" data-semantic-children="7,8,9" data-semantic-content="30,31" data-semantic-parent="33"> <mn data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-id="7" data-semantic-parent="32">1</mn> <mo data-semantic-type="punctuation" data-semantic-role="dummy" data-semantic-id="30" data-semantic-parent="32" data-semantic-added="true" data-semantic-operator="punctuated"></mo> <mrow class="MJX-TeXAtom-ORD"> <mtext data-semantic-type="text" data-semantic-role="subtraction" data-semantic-id="8" data-semantic-parent="32">-</mtext> </mrow> <mo data-semantic-type="punctuation" data-semantic-role="dummy" data-semantic-id="31" data-semantic-parent="32" data-semantic-added="true" data-semantic-operator="punctuated"></mo> <mn data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-id="9" data-semantic-parent="32">1</mn> </mrow> <mo stretchy="false" data-semantic-type="fence" data-semantic-role="close" data-semantic-id="10" data-semantic-parent="33" data-semantic-operator="fenced">)</mo> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false" data-semantic-type="fence" data-semantic-role="neutral" data-semantic-id="11" data-semantic-parent="36" data-semantic-operator="fenced">|</mo> </mrow> </mrow> <mo data-semantic-type="relation" data-semantic-role="equality" data-semantic-id="12" data-semantic-parent="40" data-semantic-operator="relseq,=">=</mo> <mrow data-semantic-type="infixop" data-semantic-role="implicit" data-semantic-id="39" data-semantic-children="18,21" data-semantic-content="38" data-semantic-parent="40"> <mrow class="MJX-TeXAtom-ORD"> <mrow data-semantic-type="vector" data-semantic-role="binomial" data-semantic-id="18" data-semantic-children="16,17" data-semantic-content="13,19" data-semantic-parent="39"> <mrow class="MJX-TeXAtom-OPEN"> <mo maxsize="2.047em" minsize="2.047em" data-semantic-type="fence" data-semantic-role="open" data-semantic-id="13" data-semantic-parent="18">(</mo> </mrow> <mfrac linethickness="0"> <mrow data-semantic-added="true" data-semantic-type="line" data-semantic-role="binomial" data-semantic-id="16" data-semantic-children="14" data-semantic-parent="18"> <mi data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-id="14" data-semantic-parent="16">k</mi> </mrow> <mrow data-semantic-added="true" data-semantic-type="line" data-semantic-role="binomial" data-semantic-id="17" data-semantic-children="15" data-semantic-parent="18"> <mi data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-id="15" data-semantic-parent="17">n</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="19" data-semantic-parent="18">)</mo> </mrow> </mrow> </mrow> <mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-id="38" data-semantic-parent="39" data-semantic-added="true" data-semantic-operator="infixop,⁢"></mo> <mi data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-id="21" data-semantic-parent="39">n</mi> </mrow> </mrow> <mo data-semantic-type="punctuation" data-semantic-role="unknown" data-semantic-id="22" data-semantic-parent="43" data-semantic-operator="punctuated">!</mo> <mrow data-semantic-type="relseq" data-semantic-role="equality" data-semantic-id="42" data-semantic-children="41,28" data-semantic-content="23" data-semantic-parent="43"> <mrow data-semantic-type="empty" data-semantic-role="unknown" data-semantic-id="41" data-semantic-parent="42"/> <mo data-semantic-type="relation" data-semantic-role="equality" data-semantic-id="23" data-semantic-parent="42" data-semantic-operator="relseq,=">=</mo> <msub data-semantic-type="subscript" data-semantic-role="leftright" data-semantic-id="28" data-semantic-children="37,27" data-semantic-parent="42" data-semantic-fencepointer="26"> <mrow data-semantic-type="fenced" data-semantic-role="leftright" data-semantic-id="37" data-semantic-children="25" data-semantic-content="24,26" data-semantic-parent="28"> <mo stretchy="false" data-semantic-type="fence" data-semantic-role="open" data-semantic-id="24" data-semantic-parent="37">(</mo> <mi data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-id="25" data-semantic-parent="37">k</mi> <mo stretchy="false" data-semantic-type="fence" data-semantic-role="close" data-semantic-id="26" data-semantic-parent="37">)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-id="27" data-semantic-parent="28">n</mi> </mrow> </msub> </mrow> </mrow> <annotation encoding="application/x-tex">|[k]^{n}(1{\text{-}}1)|={\binom {k}{n}}n!=(k)_{n}</annotation> </semantics> </math>