Solving a binomial distribution problem using polynomials

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Homework Statement
Important help on the subject of polynomials of binomial arrangement
Relevant Equations
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

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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