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Math Help - Calculating Possibilities and Combinations

  1. #1
    Newbie
    Joined
    Dec 2011
    Posts
    2

    Calculating Possibilities and Combinations

    Hi everyone,

    I have a situation which I need help calculating.

    I have 15 selections to choose from and each selection has a 50/50 ratio of being correct. I want to figure out how many combinations I can choose for each selection in order to cover all possibilities. On each of the 15 selections, one number must be chosen. For example, for the first selection, I must select 1 or 2. For the second I must select 3 or 4, etc.

    Example:

    1 - 2
    3 - 4
    5 - 6
    7 - 8
    9 - 10
    11 - 12
    13 - 14
    15 - 16
    17 - 18
    19 - 20
    21 - 22
    23 - 24
    25 - 26
    27 - 28
    29 - 30

    So one total combination is: 1-3-5-7-9-11-13-15-17-19-21-23-25-27-29. Another combination would be: 2-4-6-8-10-12-14-16-18-20-22-24-26-28-30. Another would be 1-4-6-8-10-11-14-16-17-20-21-24-26-27-30. The list goes on...so that's 3 different possibilities I just listed. Now, what I'm looking for is the total number of all combination to cover all possibilities when selecting.

    Anyone know how I can calculate this?

    Thank You,
    Dan
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  2. #2
    MHF Contributor
    Joined
    May 2010
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    28

    Re: Calculating Possibilities and Combinations

    every time you add another two-way choice, the number of possibilities doubles. so the answer is 2^n where n is the number of times you are asked to choose between 2 options.
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  3. #3
    Newbie
    Joined
    Dec 2011
    Posts
    2

    Re: Calculating Possibilities and Combinations

    Oh ok, didn't realize it was that simple...thanks a lot
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