Difference between revisions of "User:Temperal/The Problem Solver's Resource5"
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*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 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>.  *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>.  
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+  ===Ball and Urn===  
+  The ball and urn argument states that, there are this many ways to place <math>k</math> balls in <math>n</math> urns:  
+  
+  <math>{n+k1\choose n1}</math>  
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Revision as of 21:22, 10 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
Ball and UrnThe ball and urn argument states that, there are this many ways to place balls in urns:
