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Math Help - Calculating number of non consecutive numbers

  1. #1
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    Calculating number of non consecutive numbers

    Hi,

    Can someone help me with a formula that will give me the number of non consecutive numbers in a given number of events.

    So, if I had thirty selections how can I work out how many combinations of three numbers there are in the thirty selections. ie. 1,3,5 1,3,6 1,3,7 etc

    I would like a formula that allows me to put in the total number of events coupled with the number of selections. So, I would like to be able to work out, say, the number of four non consecutive groups in a total of, say, ten selections.

    As you've probably realised this is linked to some gambling probabilities. Hope you can help.

    parkingticket60
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  2. #2
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    I am not sure that I understand what you have written.
    Here is a stab at an answer.
    Consider the set of digits: \{0,1,2,3,4,5,6,7,8,9\}.
    I can select four of those with no two consecutive in \dbinom{7}{4}=\dfrac{7!}{4!\cdot 3!}=35 ways.
    We can select up to five digits with no consecutive digits.

    If you had 15 items you can select up to 8 with no two consecutive.
    For n items you can select up to \left\lceil {\frac{n}{2}} \right\rceil with no two consecutive. That is the ceiling function.
    The number of ways of selecting k items is \dbinom{n-k+1}{k}.

    If that is not what mean, please try to make is clear what you do mean.
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