Difference between revisions of "User:Temperal/The Problem Solver's Resource5"
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+ <span style="background:aqua; border:1px solid black; opacity: 0.6;fontsize:30px;position:relative;bottom:8px;borderwidth: 5px;bordercolor:blue;borderstyle: groove;position:absolute;top:50px;right:155px;width:820px;height:40px;padding:5px;">The Problem Solver's Resource</span>  + <span style="background:aqua; border:1px solid black; opacity: 0.6;fontsize:30px;position:relative;bottom:8px;borderwidth: 5px;bordercolor:blue;borderstyle: groove;position:absolute;top:50px;right:155px;width:820px;height:40px;padding:5px;">The Problem Solver's Resource</span>  
    
−   style="background:lime; border:1px solid black;height:200px;padding:10px;"  {{User:Temperal/testtemplatepage  +   style="background:lime; border:1px solid black;height:200px;padding:10px;"  {{User:Temperal/testtemplatepage 7}} 
−  ==<span style="fontsize:20px; color: blue;">  +  ==<span style="fontsize:20px; color: blue;">Combinatorics</span>== 
−  This section  +  This section cover combinatorics, and some binomial/multinomial facts. 
−  ===  +  <! will fill in later! > 
+  ===Permutations===  
+  The factorial of a number <math>n</math> is <math>n(n1)(n2)...(1)</math> or also as <math>\prod_{a=0}^{n1}(na)</math>,and is denoted by <math>n!</math>.  
−  +  Also, <math>0!=1</math>.  
−  +  The number of ways of arranging <math>n</math> distinct objects in a straight line is <math>n!</math>. This is also known as a permutation, and can be notated <math>\,_{n}P_{r}</math>  
−  +  ===Combinations===  
+  The number of ways of choosing <math>n</math> objects from a set of <math>r</math> objects is <math>\frac{n!}{r!(nr)!}</math>, which is notated as either <math>\,_{n}C_{r}</math> or <math>\binom{n}{r}</math>. (The latter notation is also known as taking the binomial coefficient.  
−  *  +  ===Binomials and Multinomials=== 
+  *Binomial Theorem: <math>(x+y)^n=\sum_{r=0}^{n}x^{nr}y^r</math>  
+  *Multinomial Coefficients: The number of ways of ordering <math>n</math> objects when <math>r_1</math> of them are of one type, <math>r_2</math> of them are of a second type, ... and <math>r_s</math> of them of another type is <math>\frac{n!}{r_1!r_2!...r_s!}</math>  
+  *Multinomial Theorem: <math>(x_1+x_2+x_3...+x_s)^n=\sum \frac{n!}{r_1!r_2!...r_s!} x_1+x_2+x_3...+x_s</math>. The summation is taken over all sums <math>\sum_{i=1}^{s}r_i</math> so that <math>\sum_{i=1}^{s}r_i=n</math>.  
−  +  [[User:Temperal/The Problem Solver's Resource6Back to page 6]]  [[User:Temperal/The Problem Solver's Resource8Continue to page 8]]  
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Revision as of 11:55, 6 October 2007
CombinatoricsThis section cover combinatorics, and some binomial/multinomial facts. PermutationsThe factorial of a number is or also as ,and is denoted by . Also, . The number of ways of arranging distinct objects in a straight line is . This is also known as a permutation, and can be notated CombinationsThe number of ways of choosing objects from a set of objects is , which is notated as either or . (The latter notation is also known as taking the binomial coefficient. Binomials and Multinomials
