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Kirkman's schoolgirl problem - deriving the conditions on n - will rep! :) Watch

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    Right, I'm a little bit iffy on the whole conditions on n and I want to know where exactly we got \frac{n-1}{2} from.

    From what I understand, we multiply r (number of days) with \frac{n}{3} (which, from my understanding, is the number of triplets of girls - let's call it k) and ^3C_2 which is the number of arrangements of pairs within each triplet, right? So then we have:

    r.(\frac{n}{3}).3 = rn... which represents what, exactly?

    Then all I know is that we equate this to ^nC_2, which is the same as \frac{n(n-1)}{2}, so finally we get

    r=\frac{n-1}{2}

    So, what I want to know is:

    • Is the reason we're dividing n by 3 because we need triplets?
    • Am I right about what ^3C_2 represents?
    • What exactly are we calculating when we do ^nC_2?


    Thanks for anyone who can clear this up for me, and rep readily available.
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    Bump... anyone?
 
 
 
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