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Ssongoku reacted to WWGD's post in the thread Finding the number of ways to arrange identical balls in a circle (3 different colors) with
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How about this: Starting with 5 identical balls, there is a total of 5!=120 arrangements. Now consider the distinction. Then: By... -
Ssongoku reacted to Gavran's post in the thread Finding the number of ways to arrange identical balls in a circle (3 different colors) with Like.
For more complicated problems than this one in the original post the formula is $$...
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Ssongoku reacted to Gavran's post in the thread Finding the number of ways to arrange identical balls in a circle (3 different colors) with Like.
You do not need any formula to solve this problem. With two blue balls and two red balls you have two cases BBRR and BRBR. How many...
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Ssongoku reacted to JimWhoKnew's post in the thread Finding the number of ways to arrange identical balls in a circle (3 different colors) with Like.
For the case 1 yellow, 2 red, 2 blue, I get 6 arrangements in a circle, which is the same as (5-1)!/(2!2!1!) . How many do you get? For...
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Ssongoku reacted to PeroK's post in the thread Finding the number of ways to arrange identical balls in a circle (3 different colors) with Like.
The idea of fixing the yellow ball is that it picks out the set of solutions that cannot be equivalent under rotation. If there were...
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Ssongoku reacted to JimWhoKnew's post in the thread Finding the number of ways to arrange identical balls in a circle (3 different colors) with Like.
Let's take a closer look at your 2 red balls and 2 blue example. The number of combinations for arranging them in a row is 4!/(2!2!)=6...
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Ssongoku reacted to WWGD's post in the thread Finding the number of ways to arrange identical balls in a circle (3 different colors) with Like.
And assume balls of the same color are undistinguishable, i.e. , b1b2= b2b1, etc.?
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Ssongoku reacted to PeroK's post in the thread Finding the number of ways to arrange identical balls in a circle (3 different colors) with Like.
I assume that two arrangements are considered equal if they are equal after rotation? If so, you could start by fixing the position of...
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Ssongoku replied to the thread Finding the number of ways to arrange identical balls in a circle (3 different colors).Yes. Let R = red ball and B = blue ball. Arrangement of BBRR in circle will be the same as BRRB So, the strategy is to list all the...
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Ssongoku posted the thread Finding the number of ways to arrange identical balls in a circle (3 different colors) in Precalculus Mathematics Homework Help.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...
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Ssongoku reacted to Greg Bernhardt's post in the thread Announcement Please welcome berkeman as PF Admin with Like.
I am thrilled and honored to announce that @berkeman has accepted a role as PF Admin! @berkeman has 20 impactful years at PF under his...
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Ssongoku replied to the thread Limit of piecewise function using epsilon delta.I am very sorry for late reply Thank you very much for all the help and explanation pasmith, PeroK, FactChecker, BvU, Gavran...
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Ssongoku reacted to FactChecker's post in the thread Limit of piecewise function using epsilon delta with Like.
Sorry, my mistake. I didn't realize that this example is different from the one in post #1. In this example, one function equation works...
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Ssongoku reacted to PeroK's post in the thread Limit of piecewise function using epsilon delta with Like.
That's not really how we are supposed to construct a proof here. Instead, for ##0<\epsilon <1##, we should let: $$\delta =...
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Ssongoku reacted to Gavran's post in the thread Limit of piecewise function using epsilon delta with Like.
The post #15 was my mistake. When ## x\to 2^- ## ## \sqrt[3]{8-\epsilon}-2\lt x-2\lt\sqrt[3]{8+\epsilon}-2 ## does not imply ##...