GMAT数学辅导：算术知识点全解析(组合)
<p> <span word="GMAT">GMAT</span>数学辅导：算术知识点全解析</p><p> 组合：<span word="combination">combination</span></p><p> <span word="A">A</span> <span word="permutation">permutation</span> <span word="can">can</span> <span word="be">be</span> <span word="thought">thought</span> <span word="of">of</span> <span word="as">as</span> <span word="a">a</span> <span word="selection">selection</span> <span word="process">process</span> <span word="in">in</span> <span word="which">which</span> <span word="objects">objects</span> <span word="are">are</span> <span word="selected">selected</span> <span word="one">one</span> <span word="by">by</span> <span word="one">one</span> <span word="in">in</span> <span word="a">a</span> <span word="certain">certain</span> <span word="order">order</span>. <span word="If">If</span> <span word="the">the</span> <span word="order">order</span> <span word="of">of</span> <span word="selection">selection</span> <span word="is">is</span> <span word="not">not</span> <span word="relevant">relevant</span> <span word="and">and</span> <span word="only">only</span> <span word="k">k</span> <span word="objects">objects</span> <span word="are">are</span> <span word="to">to</span> <span word="be">be</span> <span word="selected">selected</span> <span word="from">from</span> <span word="a">a</span> <span word="larger">larger</span> <span word="set">set</span> <span word="of">of</span> <span word="n">n</span> <span word="objects">objects</span>, <span word="a">a</span> <span word="different">different</span> <span word="counting">counting</span> <span word="method">method</span> <span word="is">is</span> <span word="employed">employed</span>.</p><p> <span word="Specially">Specially</span> <span word="consider">consider</span> <span word="a">a</span> <span word="set">set</span> <span word="of">of</span> <span word="n">n</span> <span word="objects">objects</span> <span word="from">from</span> <span word="which">which</span> <span word="a">a</span> <span word="complete">complete</span> <span word="selection">selection</span> <span word="of">of</span> <span word="k">k</span> <span word="objects">objects</span> <span word="is">is</span> <span word="to">to</span> <span word="be">be</span> <span word="made">made</span> <span word="without">without</span> <span word="regard">regard</span> <span word="to">to</span> <span word="order">order</span>, <span word="where">where</span> 0<span word="n">n</span> . <span word="Then">Then</span> <span word="the">the</span> <span word="number">number</span> <span word="of">of</span> <span word="possible">possible</span> <span word="complete">complete</span> <span word="selections">selections</span> <span word="of">of</span> <span word="k">k</span> <span word="objects">objects</span> <span word="is">is</span> <span word="called">called</span> <span word="the">the</span> <span word="number">number</span> <span word="of">of</span> <span word="combinations">combinations</span> <span word="of">of</span> <span word="n">n</span> <span word="objects">objects</span> <span word="taken">taken</span> <span word="k">k</span> <span word="at">at</span> <span word="a">a</span> <span word="time">time</span> <span word="and">and</span> <span word="is">is</span> <span word="Ckn">Ckn</span>.</p><p> 从<span word="n">n</span>个元素中任选<span word="k">k</span>个元素的数目为:</p><p> <span word="Ckn">Ckn</span>. = <span word="n">n</span>!/ ! <span word="k">k</span>!</p><p> 例如：从5个不同元素中任选2个的组合为<span word="C">C</span>25 = 5!/2! 3!= 10</p><p> 排列组合的一些特性</p><p> 加法原则：<span word="Rule">Rule</span> <span word="of">of</span> <span word="Addition">Addition</span></p><p> 做某件事有<span word="x">x</span>种方法，每种方法中又有各种不同的解决方法。例如第一种方法中有<span word="y">y</span>1种方法，第二种方法有<span word="y">y</span>2种方法，等等，第<span word="x">x</span>种方法中又有<span word="yx">yx</span>种不同的方法，每一种均可完成这件事，即它们之间的关系用<span word="or">or</span>表达，那么一般使用加法原则，即有：<span word="y">y</span>1+ <span word="y">y</span>2+。。。+ <span word="yx">yx</span>种方法。</p><p> 乘法原则：<span word="Rule">Rule</span> <span word="of">of</span> <span word="Multiplication">Multiplication</span></p><p> 完成一件事有<span word="x">x</span>个步骤，第一步有<span word="y">y</span>1种方法，第二步有<span word="y">y</span>2种方法，。。。，第<span word="x">x</span>步有<span word="yx">yx</span>种方法，完成这件事一共有<span word="y">y</span>1 <span word="y">y</span>2。。。<span word="yx">yx</span>种方法。</p>
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