Important help on the subject of polynomials of binomial arrangement

AI Thread Summary
The discussion revolves around the use of polynomials to solve binomial distribution problems, with a specific question posed by a user. An attached document, which requires Excel, contains a question that the user is struggling to solve. Clarifications were made regarding the terminology used, specifically whether "without replacement" was intended instead of "without repetition." The initial equations in the user's spreadsheet assume that balls are replaced after each draw, and two options for drawing balls were outlined. The conversation emphasizes the importance of clear definitions in mathematical problems.
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Homework Statement
Important help on the subject of polynomials of binomial arrangement
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Important help on the subject of polynomials of binomial arrangement
[Mentor Note -- Multiple threads merged. @issue -- please do not cross-post your threads]

Hi, everyone
It is known that binomial distribution can also be solved by polynomials. i add document with a question I can not solve.

Glad to get for help

Thanks to all the respondents
 

Attachments

Last edited by a moderator:
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Hi, everyone
It is known that binomial distribution can also be solved by polynomials. i add document with a question I can not solve.

Glad to get for help

Thanks to all the respondents
 

Attachments

Two points of clarification before proceeding:
  1. The attached file requires Excel.
  2. Possible typo. Did you mean "without replacement" instead of "without repetition"?.
If I read the question correctly, the initial equations in the spreadsheet assume replacement of the colored balls after each choice.
 
Point refinement: There are 2 options 1. Take out a ball and return it to the basket 2. Find a ball and do not return it to the basket

By the way thank you very much for the quick response. it's not taken for granted
 
Klystron said:
Two points of clarification before proceeding:
  1. The attached file requires Excel.
  2. Possible typo. Did you mean "without replacement" instead of "without repetition"?.
If I read the question correctly, the initial equations in the spreadsheet assume replacement of the colored balls after each choice.
Point refinement: There are 2 options 1. Take out a ball and return it to the basket 2. Find a ball and do not return it to the basket

By the way thank you very much for the quick response. it's not taken for granted
 

Thread 'Finding the number of ways to arrange identical balls in a circle'

I tried to combine those 2 formulas but it didn't work. I tried using another case where there are 2 red balls and 2 blue balls only so when combining the formula I got ##\frac{(4-1)!}{2!2!}=\frac{3}{2}## which does not make sense. Is there any formula to calculate cyclic permutation of identical objects or I have to do it by listing all the possibilities? Thanks
View full post »

Thread 'Making the denominator of a certain fraction real'

Essentially I just have this problem that I'm stuck on, on a sheet about complex numbers: Show that, for ##|r|<1,## $$1+r\cos(x)+r^2\cos(2x)+r^3\cos(3x)...=\frac{1-r\cos(x)}{1-2r\cos(x)+r^2}$$ My first thought was to express it as a geometric series, where the real part of the sum of the series would be the series you see above: $$1+re^{ix}+r^2e^{2ix}+r^3e^{3ix}...$$ The sum of this series is just: $$\frac{(re^{ix})^n-1}{re^{ix} - 1}$$ I'm having some trouble trying to figure out what to...
View full post »

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