Permutation of Different Cards (Distinguishable Objects)
2014-02-05 08:00
This GeoGebra applet simulates how different distinguishable objects can be arranged to obtain various permutations. Users can adjust the number of cards from 2 to 4 using sliders to visually observe and calculate full permutations. Utilizing sequence and list commands, this interactive tool vividly demonstrates the concept of permutations in combinatorics, helping students understand the principl
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<show object="true" label="true"/>
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<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"/>
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<command name="Sequence">
<input a0="Mod[24 - i, 6]" a1="i" a2="1" a3="24"/>
<output a0="Y0Set"/>
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<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"/>
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<command name="Sequence">
<input a0="ceil(i / 6)" a1="i" a2="1" a3="24"/>
<output a0="X0Set"/>
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<element type="list" label="X0Set">
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<lineStyle thickness="2" type="0" typeHidden="1"/>
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<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"/>
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<command name="Element">
<input a0="XSep" a1="NObj"/>
<output a0="XSeparation"/>
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<element type="numeric" label="XSeparation">
<value val="4.5"/>
<objColor r="0" g="0" b="0" alpha="0.1"/>
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<command name="Element">
<input a0="YScale" a1="NObj"/>
<output a0="YScal"/>
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<element type="numeric" label="YScal">
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<objColor r="0" g="0" b="0" alpha="0.1"/>
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<command name="Element">
<input a0="XScale" a1="NObj"/>
<output a0="XScal"/>
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<element type="numeric" label="XScal">
<value val="1.1"/>
<objColor r="0" g="0" b="0" alpha="0.1"/>
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<expression label ="List311" exp="{1, 2, 3}"/>
<element type="list" label="List311">
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<lineStyle thickness="2" type="0" typeHidden="1"/>
<pointSize val="3"/>
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<element type="list" label="List312">
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<animation step="1" speed="1" type="0" playing="false"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<pointSize val="3"/>
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<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"/>
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<expression label ="List314" exp="{2, 3, 1}"/>
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<lineStyle thickness="2" type="0" typeHidden="1"/>
<pointSize val="3"/>
<pointStyle val="-1"/>
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<expression label ="List315" exp="{3, 1, 2}"/>
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<expression label="Permute3" exp="{List311, List312, List313, List315, List314, List316}" />
<element type="list" label="Permute3">
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<lineStyle thickness="2" type="0" typeHidden="1"/>
<pointSize val="3"/>
<pointStyle val="-1"/>
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<expression label ="List211" exp="{1, 2}"/>
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<animation step="1" speed="1" type="0" playing="false"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<pointSize val="3"/>
<pointStyle val="-1"/>
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<expression label ="List212" exp="{2, 1}"/>
<element type="list" label="List212">
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<animation step="1" speed="1" type="0" playing="false"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<pointSize val="3"/>
<pointStyle val="-1"/>
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<expression label="Permute2" exp="{List211, List212}" />
<element type="list" label="Permute2">
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<lineStyle thickness="2" type="0" typeHidden="1"/>
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<pointStyle val="-1"/>
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<expression label ="List111" exp="{1}"/>
<element type="list" label="List111">
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<animation step="1" speed="1" type="0" playing="false"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<pointSize val="3"/>
<pointStyle val="-1"/>
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<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"/>
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<expression label ="List200" exp="{1, 2}"/>
<element type="list" label="List200">
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<animation step="1" speed="1" type="0" playing="false"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<pointSize val="3"/>
<pointStyle val="-1"/>
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<expression label ="List300" exp="{1, 2, 3}"/>
<element type="list" label="List300">
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<lineStyle thickness="2" type="0" typeHidden="1"/>
<pointSize val="3"/>
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<expression label ="List100" exp="{1}"/>
<element type="list" label="List100">
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<animation step="1" speed="1" type="0" playing="false"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<pointSize val="3"/>
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<expression label="List00" exp="{List100, List200, List300, List400}" />
<element type="list" label="List00">
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<lineStyle thickness="2" type="0" typeHidden="1"/>
<pointSize val="3"/>
<pointStyle val="-1"/>
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<command name="Sequence">
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<expression label="YY" exp="FindCor(k, 0, 10, Element[List400, 3], Element[Element[Permute4, 3], 2])" />
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