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📁 组合数学 清华大学研究生课程课件 呵呵
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<p style='margin-left:18.0pt;text-indent:-18.0pt;mso-list:l0 level1 lfo1;
tab-stops:list 18.0pt'><![if !supportLists]><span lang=EN-US>1．</span><![endif]>证明等式
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<p>解法一：利用第一章的第<span lang=EN-US>8节的公式7：令m = n, r = n即可。</span></p>

<p>解法二：观察母函数<span lang=EN-US><span style='mso-text-raise:-12.0pt'><!--[if gte vml 1]><v:shape
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</xml><![endif]-->的常数项（或是利用恒等式<span style='mso-text-raise:-5.0pt'><!--[if gte vml 1]><v:shape
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</v:shape><![endif]--><![if !vml]><img width=174 height=24
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</xml><![endif]-->，比较两边<span style='mso-text-raise:-3.0pt'><!--[if gte vml 1]><v:shape
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<p>都可以得到结论。</p>

<p><span lang=EN-US>2.求(1+x<sup>4</sup>+x<sup>8</sup>)<sup> 100</sup>中x<sup>20</sup>项的系数.&nbsp;</span></p>

<p>解法一：分析<span lang=EN-US>(x<sup>4</sup>+x<sup>8</sup>)<sup>k</sup>的结构可知仅当k=3,4,5时有x<sup>20</sup>项&nbsp;，三个系数相加即为所求</span></p>

<p>解法二：直接进行多项式的展开：<span lang=EN-US><span style='mso-text-raise:-15.0pt'><!--[if gte vml 1]><v:shape
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<p>所以<span lang=EN-US><span style='mso-text-raise:-3.0pt'><!--[if gte vml 1]><v:shape
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</v:shape><![endif]--><![if !vml]><img width=24 height=21
src="./timu.files/image012.gif" v:shapes="_x0000_i1196"><![endif]></span><!--[if gte mso 9]><xml>
 <o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1196"
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</xml><![endif]-->的系数为<span style='mso-text-raise:-23.0pt'><!--[if gte vml 1]><v:shape
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</v:shape><![endif]--><![if !vml]><img width=308 height=59
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<p><span lang=EN-US>3.有红、黄、蓝、白球各两个，绿、紫、 黑的球各3个，问从中取出10个球，试问 有多少种不同的取法？&nbsp;</span></p>

<p>解：用指数型母函数，可得母函数<span lang=EN-US><span style='mso-text-raise:-16.0pt'><!--[if gte vml 1]><v:shape
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</v:shape><![endif]--><![if !vml]><img width=222 height=54
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<p><span lang=EN-US>&nbsp; 项<span style='mso-text-raise:-12.0pt'><!--[if gte vml 1]><v:shape
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