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Math Help - Combinational Methods help

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    Combinational Methods help

    Hey everyone,

    I just started my statistics course and I'm having trouble with one of the questions. I was hoping that somebody could give me some insight into completing one of the first ones, because every question after it references back to it.

    Here's the question:

    "An operation consists of two steps, of which the first can be made in n_{1} ways. If the first step is made in the ith way, the step step can be made in the n_{2i} ways.

    A) Use a tree diagram to find a formula for the total number of ways in which the total operation can be made.

    B) A student can study 0, 1, 2, or 3 hours for a history test on any given day. Use the formula obtained in part A to verify that there are 13 ways in which the student can study at most 4 hours for the test on two consecutive days."


    The formula in the back of the book is

    \sum_{i=1}^n{n_{2i}} (that n on top should be n_{i} but I can't seem to get it to show up that way, hope it still makes sense)

    which I sort of understand, but if somebody could give me a more thorough explanation I certainly would appreciate it.

    For the tree diagram, I believe I drew it correct, but I don't know how to apply the formula to this question. I'm just stuck overall.

    Any bits of help are greatly appreciated, thanks!
    Last edited by billb91; September 2nd 2013 at 03:50 PM.
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