GingerAle

Tthe number of ways of choosing three people in a circular table with 12 people, so that no two people are next to each other.

Solution:

There are 12 ways to choose 3 persons who are adjacent (next to each other).

There are 12 ways to choose 2 persons who are adjacent.

There are 8 ways to choose 1 person who is not adjacent to the other two (2).

There are nCr(12,3) to choose a set of three persons from set of 12.

Subtract the persons who are adjacent from the total sets.

\(\text{So then ... } \dbinom {12}{3} - 12 - (12*8) = 112\\ \small \text{ There are 112 ways to select three persons from a set of 12 seated in a circle, such that no two persons are adjacent. }\\\)

GA

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Max, your monographic summary analysis on binomial theory is amazing! It’s one of the best I’ve read anywhere. 

It’s wonderful you have returned! I hope you stay around for awhile.

I will let you figure out the rest.

I don’t know if the OP student will choose to figure out the rest, but I sure as hell will.

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You may find this formula interesting.

\(\sum \limits_{k=0}^{m}\binom{n}{k} (-1)^k \binom{p – s*k – 1}{p – s*k – n} \leftarrow \text {where p is the point (sum) target, n is the # of die, }\\ \hspace {47mm} \text{s is the number of sides, and } m=\lfloor \dfrac{p-n}{s}\rfloor \\\)

This formula is from J. V. Uspensky’s Introduction to Mathematical Probability (1937).

This calculates the number of combinations for any given sum of pips on (N) number of dice with (S) sides, where each die-side has a unique number of pips from 1 to (S)

You’re too dumb to know this is not a question....

GA

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Oh... I can still do that ...I’d just create guest accounts.

In any case, there’s no need for a chipmunk to visit you, a shrew or titmouse is more than adequate.

BTW, Amazon has curling irons on sale this month. Get the one for banana curls. It works best for cauterizing big assholes....

GA

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humm... Instead of coming here to get fucked, you should ask your AI the best way to fuck yourself.

For you, it will recommend a curling iron set on HIGH. That’s the setting used to cauterize assholes...

GA

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For the record: "TheGingeriousAle" account is not under the control GingerAle.

.... I was wondering when you’d return... and what user name you’d create to impersonate GingerAle.  TheGingeriousAle is a likeable name. I’m rather amazed an obnoxious and noxious troll could create the name. ...Perhaps you didn’t. If you used an AI then it’s not really your creation. 

You posted a correct math solution (without bullshit), which is also amazing...and you didn’t sign my initials. Is this a change in tactics or will the familiar “other shoe” drop in a future post?

...In any case, impersonating another member is a violation of the TOS. So this account, like all the others impersonating GingerAle, is subject to banning. ...And banned it will be, eventually...

GA

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For the record: Post #1, signed by GA, is not by the real GA.

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History is ten eleven years of age. ...and he is very intelligent.  I suspect he’ll have a solid handle on calculus by middle school ....and have viable solutions for world hunger by the time he graduates from university at 16. 

GA

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