Probability problem, very hard

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The discussion revolves around a challenging probability problem, with participants referencing two related problems. Problem 2 is noted to be easier if Problem 1 has been solved, suggesting a conceptual link between them. One participant expresses frustration in finding a solution to the problems, indicating difficulty in understanding the concepts. Ultimately, they mention resolving the issue and express gratitude for the assistance received. The thread highlights the interconnected nature of the problems and the challenges faced by those attempting to solve them.
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Have you done problem 1? Problem 2 says "This one may seem easy/trivial if you have completed problem 1, since it is looking at the same problem in just a slightly different way."
Look back at how you did problem 1 and see if you can tell how it applies.
 
hi

i don't know. really i tried and tried . can't seem to find a right answer or to resolve it.
 
you can delete the post if u want to. i resolve the problem and thanks u for everything
 

Thread 'Finding the number of ways to arrange identical balls in a circle (3 different colors)'

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
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Thread 'Greatest possible value of a constant in polynomial'

Since ##px^9+q## is the factor, then ##x^9=\frac{-q}{p}## will be one of the roots. Let ##f(x)=27x^{18}+bx^9+70##, then: $$27\left(\frac{-q}{p}\right)^2+b\left(\frac{-q}{p}\right)+70=0$$ $$b=27 \frac{q}{p}+70 \frac{p}{q}$$ $$b=\frac{27q^2+70p^2}{pq}$$ From this expression, it looks like there is no greatest value of ##b## because increasing the value of ##p## and ##q## will also increase the value of ##b##. How to find the greatest value of ##b##? Thanks
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