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: | ||
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+ | <math>{n+k-1\choose n-1}</math> | ||
[[User:Temperal/The Problem Solver's Resource4|Back to page 4]] | [[User:Temperal/The Problem Solver's Resource6|Continue to page 6]] | [[User:Temperal/The Problem Solver's Resource4|Back to page 4]] | [[User:Temperal/The Problem Solver's Resource6|Continue to page 6]] | ||
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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 Also, The number of ways of arranging CombinationsThe number of ways of choosing Binomials and Multinomials
Ball and UrnThe ball and urn argument states that, there are this many ways to place
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