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160 lines
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HTML
160 lines
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HTML
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<h1 align="center">The Basic Counting Principle</h1>
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<div class="def">
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<p align="center">When there are <span class="larger"><b>m</b></span> ways to do one thing, <br />
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and <span class="larger"><b>n</b></span> ways to do another, <br />
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then there are <span class="larger"><b>m×n</b></span> ways of doing <b>both</b>.</p>
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</div>
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<p> </p>
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<div class="example">
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<p>Example: you have <b>3</b> shirts and <b>4</b> pants. </p>
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<p>That means <b>3×4=12</b> different outfits.</p>
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</div>
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<div class="example">
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<p>Example: There are <b>6</b> flavors of ice-cream, and <b>3</b> different cones. </p>
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<p>That means <b>6×3=18</b> different single-scoop ice-creams you could order.</p>
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</div>
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<p>It also works when you have more than 2 choices:</p>
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<div class="example">
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<h3>Example: You are buying a new car.</h3>
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<table border="0">
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<tr>
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<td valign="top">There are <b>2</b> body styles:</td>
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<td valign="top"> </td>
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<td align="center"><img src="images/tree-car-choices-body.gif" alt="Car Choices" width="262" height="46" /><br />
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<span class="larger">sedan or hatchback</span> </td>
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</tr>
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<tr>
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<td valign="top"> </td>
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<td valign="top"> </td>
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<td align="center"> </td>
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</tr>
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<tr>
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<td valign="top">There are <b>5</b> colors available:</td>
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<td valign="top"> </td>
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<td align="center"><img src="images/tree-car-choices-colors.gif" alt="Car Choices" width="267" height="35" /></td>
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</tr>
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<tr>
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<td valign="top"> </td>
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<td valign="top"> </td>
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<td align="center"> </td>
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</tr>
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<tr>
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<td valign="top">There are <b>3</b> models: </td>
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<td valign="top"> </td>
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<td><ul>
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<li>GL (standard model), </li>
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<li>SS (sports model with bigger engine)</li>
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<li>SL (luxury model with leather seats)</li>
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</ul></td>
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</tr>
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</table>
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<p class="large">How many total choices?</p>
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<p>You can see in this "tree" diagram:</p>
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<p class="center"><img src="images/tree-car-choices.svg" alt="Car Choices" /></p>
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<p>You can count the choices, or just do the simple calculation:</p>
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<p align="center" class="larger">Total Choices = 2 <b>×</b> 5 <b>×</b> 3 = 30</p>
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</div>
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<h2>Independent or Dependent?</h2>
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<p>But it only works when all choices are <b>independent</b> of each other. </p>
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<p>If one choice affects another choice (i.e. <b>depends</b> on another choice), then a simple multiplication is not right.</p>
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<div class="example">
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<h3>Example: You are buying a new car ... but ...</h3>
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<p>the salesman says <b>"You can't choose black for the hatchback"</b> ... well then things change!</p>
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<p class="center"><img src="images/tree-car-choices-2.svg" alt="Car Choices, one not available" /></p>
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<p align="center" class="larger">You now have only 27 choices.</p>
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<p>Because your choices are <b>not independent</b> of each other.</p>
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<p>But you can still make your life easier with this calculation:</p>
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<p align="center" class="larger">Choices = 5<b>×</b>3 + 4<b>×</b>3 = 15 + 12 = 27</p>
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</div>
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<p> </p>
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