GMAT数学辅导：算术知识点全解析(排列)
<p> <span word="GMAT">GMAT</span>数学辅导：算术知识点全解析</p><p> 6.排列与组合</p><p> <span word="There">There</span> <span word="are">are</span> <span word="some">some</span> <span word="useful">useful</span> <span word="methods">methods</span> <span word="for">for</span> <span word="counting">counting</span> <span word="objects">objects</span> <span word="and">and</span> <span word="sets">sets</span> <span word="of">of</span> <span word="objects">objects</span> <span word="without">without</span> <span word="actually">actually</span> <span word="listing">listing</span> <span word="the">the</span> <span word="elements">elements</span> <span word="to">to</span> <span word="be">be</span> <span word="counted">counted</span>. <span word="The">The</span> <span word="following">following</span> <span word="principle">principle</span> <span word="of">of</span> <span word="Multiplication">Multiplication</span> <span word="is">is</span> <span word="fundamental">fundamental</span> <span word="to">to</span> <span word="these">these</span> <span word="methods">methods</span>.</p><p> <span word="If">If</span> <span word="a">a</span> <span word="first">first</span> <span word="object">object</span> <span word="may">may</span> <span word="be">be</span> <span word="chosen">chosen</span> <span word="in">in</span> <span word="m">m</span> <span word="ways">ways</span> <span word="and">and</span> <span word="a">a</span> <span word="second">second</span> <span word="object">object</span> <span word="may">may</span> <span word="be">be</span> <span word="chosen">chosen</span> <span word="in">in</span> <span word="n">n</span> <span word="ways">ways</span>, <span word="then">then</span> <span word="there">there</span> <span word="are">are</span> <span word="mn">mn</span> <span word="ways">ways</span> <span word="of">of</span> <span word="choosing">choosing</span> <span word="both">both</span> <span word="objects">objects</span>.</p><p> <span word="As">As</span> <span word="an">an</span> <span word="example">example</span>, <span word="suppose">suppose</span> <span word="the">the</span> <span word="objects">objects</span> <span word="are">are</span> <span word="items">items</span> <span word="on">on</span> <span word="a">a</span> <span word="menu">menu</span>. <span word="If">If</span> <span word="a">a</span> <span word="meal">meal</span> <span word="consists">consists</span> <span word="of">of</span> <span word="one">one</span> <span word="entree">entree</span> <span word="and">and</span> <span word="one">one</span> <span word="dessert">dessert</span> <span word="and">and</span> <span word="there">there</span> <span word="are">are</span> 5 <span word="entrees">entrees</span> <span word="and">and</span> 3 <span word="desserts">desserts</span> <span word="on">on</span> <span word="the">the</span> <span word="menu">menu</span>, <span word="then">then</span> 53 = 15 <span word="different">different</span> <span word="meals">meals</span> <span word="can">can</span> <span word="be">be</span> <span word="ordered">ordered</span> <span word="from">from</span> <span word="the">the</span> <span word="menu">menu</span>. <span word="As">As</span> <span word="another">another</span> <span word="example">example</span>, <span word="each">each</span> <span word="time">time</span> <span word="a">a</span> <span word="coin">coin</span> <span word="is">is</span> <span word="flipped">flipped</span>, <span word="there">there</span> <span word="are">are</span> <span word="two">two</span> <span word="possible">possible</span> <span word="outcomes">outcomes</span>, <span word="heads">heads</span> <span word="and">and</span> <span word="tails">tails</span>. <span word="If">If</span> <span word="an">an</span> <span word="experiment">experiment</span> <span word="consists">consists</span> <span word="of">of</span> 8 <span word="consecutive">consecutive</span> <span word="coin">coin</span> <span word="flips">flips</span>, <span word="the">the</span> <span word="experiment">experiment</span> <span word="has">has</span> 28 <span word="possible">possible</span> <span word="outcomes">outcomes</span>, <span word="where">where</span> <span word="each">each</span> <span word="of">of</span> <span word="these">these</span> <span word="outcomes">outcomes</span> <span word="is">is</span> <span word="a">a</span> <span word="list">list</span> <span word="of">of</span> <span word="heads">heads</span> <span word="and">and</span> <span word="tails">tails</span> <span word="in">in</span> <span word="some">some</span> <span word="order">order</span>.</p><p> 阶乘：<span word="factorial">factorial</span> <span word="notation">notation</span></p><p> 假如一个大于1的整数<span word="n">n</span>，计算<span word="n">n</span>的阶乘被表示为<span word="n">n</span>!，被定义为从1至<span word="n">n</span>所有整数的乘积，</p><p> 例如：4! = 4321= 24</p><p> 注意：0! = 1! = 1</p><p> 排列：<span word="permutations">permutations</span></p><p> <span word="The">The</span> <span word="factorial">factorial</span> <span word="is">is</span> <span word="useful">useful</span> <span word="for">for</span> <span word="counting">counting</span> <span word="the">the</span> <span word="number">number</span> <span word="of">of</span> <span word="ways">ways</span> <span word="that">that</span> <span word="a">a</span> <span word="set">set</span> <span word="of">of</span> <span word="objects">objects</span> <span word="can">can</span> <span word="be">be</span> <span word="ordered">ordered</span>. <span word="If">If</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="is">is</span> <span word="to">to</span> <span word="be">be</span> <span word="ordered">ordered</span> <span word="from">from</span> 1<span word="st">st</span> <span word="to">to</span> <span word="nth">nth</span>, <span word="there">there</span> <span word="are">are</span> <span word="n">n</span> <span word="choices">choices</span> <span word="for">for</span> <span word="the">the</span> 1<span word="st">st</span> <span word="object">object</span>, <span word="n">n</span>-1 <span word="choices">choices</span> <span word="for">for</span> <span word="the">the</span> 2<span word="nd">nd</span> <span word="object">object</span>, <span word="n">n</span>-2 <span word="choices">choices</span> <span word="for">for</span> <span word="the">the</span> 3<span word="rd">rd</span> <span word="object">object</span>, <span word="and">and</span> <span word="so">so</span> <span word="on">on</span>, <span word="until">until</span> <span word="there">there</span> <span word="is">is</span> <span word="only">only</span> 1 <span word="choice">choice</span> <span word="for">for</span> <span word="the">the</span> <span word="nth">nth</span> <span word="object">object</span>. <span word="Thus">Thus</span>, <span word="by">by</span> <span word="the">the</span> <span word="multiplication">multiplication</span> <span word="principle">principle</span>, <span word="the">the</span> <span word="number">number</span> <span word="of">of</span> <span word="ways">ways</span> <span word="of">of</span> <span word="ordering">ordering</span> <span word="the">the</span> <span word="n">n</span> <span word="objects">objects</span> <span word="is">is</span></p>
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