不同卡片的排列（可区分对象）
2014-02-05 08:00
本GeoGebra范例演示了如何对不同的可区分对象进行排列以获得不同的排列数。用户可以通过滑块调整卡片数量（2至4张），直观地观察和计算全排列的情况。该互动课件结合了序列与列表命令，生动展示了组合数学中的排列概念，帮助学生理解阶乘与排列数的计算原理。
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<expression label="Permute4" exp="{List411, List412, List413, List415, List414, List416, List421, List422, List431, List441, List432, List442, List423, List425, List433, List443, List435, List445, List424, List426, List434, List444, List436, List446}" />
<element type="list" label="Permute4">
<objColor r="0" g="100" b="0" alpha="0.1"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<pointSize val="3"/>
<pointStyle val="-1"/>
</element>
<element type="numeric" label="k">
<value val="0.0"/>
<show object="true" label="true"/>
<objColor r="0" g="0" b="0" alpha="0.1"/>
<layer val="0"/>
<labelMode val="1"/>
<slider min="0" max="NObj!" absoluteScreenLocation="true" width="430.0" x="535.0" y="89.0" fixed="false" horizontal="true"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<animation step="0.1" speed="1" type="0" playing="false"/>
</element>
<command name="Sequence">
<input a0="Mod[24 - i, 6]" a1="i" a2="1" a3="24"/>
<output a0="Y0Set"/>
</command>
<element type="list" label="Y0Set">
<objColor r="0" g="100" b="0" alpha="0.1"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<pointSize val="3"/>
<pointStyle val="-1"/>
</element>
<command name="Sequence">
<input a0="ceil(i / 6)" a1="i" a2="1" a3="24"/>
<output a0="X0Set"/>
</command>
<element type="list" label="X0Set">
<objColor r="0" g="100" b="0" alpha="0.1"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<pointSize val="3"/>
<pointStyle val="-1"/>
</element>
<element type="numeric" label="NObj">
<value val="2.0"/>
<show object="true" label="false"/>
<objColor r="0" g="0" b="0" alpha="0.1"/>
<layer val="0"/>
<labelOffset x="80" y="-1"/>
<labelMode val="2"/>
<slider min="2" max="4" absoluteScreenLocation="true" width="150.0" x="26.0" y="89.0" fixed="false" horizontal="true"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<animation step="1" speed="1" type="0" playing="false"/>
<ggbscript onUpdate="k=0 Tree=1"/>
</element>
<command name="Element">
<input a0="XSep" a1="NObj"/>
<output a0="XSeparation"/>
</command>
<element type="numeric" label="XSeparation">
<value val="4.5"/>
<objColor r="0" g="0" b="0" alpha="0.1"/>
</element>
<command name="Element">
<input a0="YScale" a1="NObj"/>
<output a0="YScal"/>
</command>
<element type="numeric" label="YScal">
<value val="1.3"/>
<objColor r="0" g="0" b="0" alpha="0.1"/>
</element>
<command name="Element">
<input a0="XScale" a1="NObj"/>
<output a0="XScal"/>
</command>
<element type="numeric" label="XScal">
<value val="1.1"/>
<objColor r="0" g="0" b="0" alpha="0.1"/>
</element>
<expression label ="List311" exp="{1, 2, 3}"/>
<element type="list" label="List311">
<objColor r="0" g="100" b="0" alpha="0.1"/>
<animation step="1" speed="1" type="0" playing="false"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<pointSize val="3"/>
<pointStyle val="-1"/>
</element>
<expression label ="List312" exp="{1, 3, 2}"/>
<element type="list" label="List312">
<objColor r="0" g="100" b="0" alpha="0.1"/>
<animation step="1" speed="1" type="0" playing="false"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<pointSize val="3"/>
<pointStyle val="-1"/>
</element>
<expression label ="List313" exp="{2, 1, 3}"/>
<element type="list" label="List313">
<objColor r="0" g="100" b="0" alpha="0.1"/>
<animation step="1" speed="1" type="0" playing="false"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<pointSize val="3"/>
<pointStyle val="-1"/>
</element>
<expression label ="List314" exp="{2, 3, 1}"/>
<element type="list" label="List314">
<objColor r="0" g="100" b="0" alpha="0.1"/>
<animation step="1" speed="1" type="0" playing="false"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<pointSize val="3"/>
<pointStyle val="-1"/>
</element>
<expression label ="List315" exp="{3, 1, 2}"/>
<element type="list" label="List315">
<objColor r="0" g="100" b="0" alpha="0.1"/>
<animation step="1" speed="1" type="0" playing="false"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<pointSize val="3"/>
<pointStyle val="-1"/>
</element>
<expression label ="List316" exp="{3, 2, 1}"/>
<element type="list" label="List316">
<objColor r="0" g="100" b="0" alpha="0.1"/>
<animation step="1" speed="1" type="0" playing="false"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<pointSize val="3"/>
<pointStyle val="-1"/>
</element>
<expression label="Permute3" exp="{List311, List312, List313, List315, List314, List316}" />
<element type="list" label="Permute3">
<objColor r="0" g="100" b="0" alpha="0.1"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<pointSize val="3"/>
<pointStyle val="-1"/>
</element>
<expression label ="List211" exp="{1, 2}"/>
<element type="list" label="List211">
<objColor r="0" g="100" b="0" alpha="0.1"/>
<animation step="1" speed="1" type="0" playing="false"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<pointSize val="3"/>
<pointStyle val="-1"/>
</element>
<expression label ="List212" exp="{2, 1}"/>
<element type="list" label="List212">
<objColor r="0" g="100" b="0" alpha="0.1"/>
<animation step="1" speed="1" type="0" playing="false"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<pointSize val="3"/>
<pointStyle val="-1"/>
</element>
<expression label="Permute2" exp="{List211, List212}" />
<element type="list" label="Permute2">
<objColor r="0" g="100" b="0" alpha="0.1"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<pointSize val="3"/>
<pointStyle val="-1"/>
</element>
<expression label ="List111" exp="{1}"/>
<element type="list" label="List111">
<objColor r="0" g="100" b="0" alpha="0.1"/>
<animation step="1" speed="1" type="0" playing="false"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<pointSize val="3"/>
<pointStyle val="-1"/>
</element>
<expression label="Permute1" exp="{List111}" />
<element type="list" label="Permute1">
<objColor r="0" g="100" b="0" alpha="0.1"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<pointSize val="3"/>
<pointStyle val="-1"/>
</element>
<expression label="Permute" exp="{Permute1, Permute2, Permute3, Permute4}" />
<element type="list" label="Permute">
<objColor r="0" g="100" b="0" alpha="0.1"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<pointSize val="3"/>
<pointStyle val="-1"/>
</element>
<expression label ="List200" exp="{1, 2}"/>
<element type="list" label="List200">
<objColor r="0" g="100" b="0" alpha="0.1"/>
<animation step="1" speed="1" type="0" playing="false"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<pointSize val="3"/>
<pointStyle val="-1"/>
</element>
<expression label ="List300" exp="{1, 2, 3}"/>
<element type="list" label="List300">
<objColor r="0" g="100" b="0" alpha="0.1"/>
<animation step="1" speed="1" type="0" playing="false"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<pointSize val="3"/>
<pointStyle val="-1"/>
</element>
<expression label ="List100" exp="{1}"/>
<element type="list" label="List100">
<objColor r="0" g="100" b="0" alpha="0.1"/>
<animation step="1" speed="1" type="0" playing="false"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<pointSize val="3"/>
<pointStyle val="-1"/>
</element>
<expression label="List00" exp="{List100, List200, List300, List400}" />
<element type="list" label="List00">
<objColor r="0" g="100" b="0" alpha="0.1"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<pointSize val="3"/>
<pointStyle val="-1"/>
</element>
<command name="Sequence">
<input a0="Sequence[(XScal * (Element[X0Set, i] * XSeparation + If[k < i - 1, Element[Element[List00, NObj], j], If[k > i, Element[Element[Element[Permute, NObj], i], j], FindCor(k, i - 1, i, Element[Element[List00, NObj], j], Element[Element[Element[Permute, NObj], i], j])]]), YScal * Element[Y0Set, i]), j, 1, NObj]" a1="i" a2="1" a3="NObj!"/>
<output a0="PointSet"/>
</command>
<element type="list" label="PointSet">
<show object="false" label="true"/>
<objColor r="0" g="100" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<pointSize val="3"/>
<pointStyle val="-1"/>
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<cascell caslabel="a" >
<cellPair>
<inputCell>
<expression value="a(k,x1,x2,y1,y2):=y1+(y2-y1)/(x2-x1)*(k-x1)" />
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<outputCell>
<expression value="a(k, x1, x2, y1, y2):=(k * y1 - k * y2 + x1 * y2 - x2 * y1) / (x1 - x2)" native="true"/>
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</cascell>
<expression label="a" exp="a(k, x1, x2, y1, y2) = (k * y1 - k * y2 + x1 * y2 - x2 * y1) / (x1 - x2)" />
<element type="functionNVar" label="a">
<show object="true" label="false"/>
<objColor r="255" g="0" b="0" alpha="0.75"/>
<layer val="0"/>
<labelMode val="0"/>
</element>
<expression label="YY" exp="FindCor(k, 0, 10, Element[List400, 3], Element[Element[Permute4, 3], 2])" />
<element type="numeric" label="YY">
<value val="3.0"/>
<objColor r="0" g="100" b="0" alpha="0.1"/>
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<file name="e5f2479a9d3b8f867abbb782dfc30c8e\01_McDull03.jpg"/>
<inBackground val="false"/>
<startPoint number="0" exp="Element[Element[PointSet, 1], 1]"/>
<show object="true" label="true"/>
<condition showObject="¬d"/>
<objColor r="0" g="0" b="0" alpha="1.0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="1" speed="1" type="0" playing="false"/>
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<element type="image" label="zpic02">
<file name="e5f2479a9d3b8f867abbb782dfc30c8e\01_McDull03.jpg"/>
<inBackground val="false"/>
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<layer val="0"/>
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<element type="image" label="zpic03">
<file name="e5f2479a9d3b8f867abbb782dfc30c8e\01_McDull03.jpg"/>
<inBackground val="false"/>
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<element type="image" label="zpic04">
<file name="e5f2479a9d3b8f867abbb782dfc30c8e\01_McDull03.jpg"/>
<inBackground val="false"/>
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<element type="image" label="zpic05">
<file name="e5f2479a9d3b8f867abbb782dfc30c8e\01_McDull03.jpg"/>
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<element type="image" label="zpic06">
<file name="e5f2479a9d3b8f867abbb782dfc30c8e\01_McDull03.jpg"/>
<inBackground val="false"/>
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<element type="image" label="zpic07">
<file name="e5f2479a9d3b8f867abbb782dfc30c8e\01_McDull03.jpg"/>
<inBackground val="false"/>
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<element type="image" label="zpic08">
<file name="e5f2479a9d3b8f867abbb782dfc30c8e\01_McDull03.jpg"/>
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<element type="image" label="zpic10">
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<input a0="Element[GPoint, 1] + (0, 0.5)" a1="Element[GPoint, 6] - (0, 0.5)"/>
<output a0="e"/>
</command>
<element type="segment" label="e">
<show object="true" label="false"/>
<condition showObject="NObj ≟ 3 ∧ (Tree ≥ 12)"/>
<objColor r="128" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="6.6" y="0.0" z="-137.28"/>
<lineStyle thickness="5" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
</construction>
</geogebra>