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Math Help - Calculating the amount of possibilities

  1. #1
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    Jun 2012
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    Québec
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    Calculating the amount of possibilities

    Hi there,

    I need some help to resolve a problem... Let's say that I have 30 options spread in 3 blocks where a person need to choose 10 options according to these rules:
    1. The person can only choose 3 options in the last block
    2. The person can only choose 3 options in the second block
    3. There is no maximum related to the first block
    4. The previous block must always have equal or less options chosen (example: cannot take 3 options in 3rd block if 2nd block has only 2 options picked)
    5. The number of options per block is variable, for the first sequence the 1st block could have 10, for the 2nd sequence the 1st block could have 7 etc.
    6. An option can be picked only once


    If someone might have some idea on how to resolve this, I'd really appreciate it.

    Thanks !
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  2. #2
    Newbie
    Joined
    Jun 2012
    From
    New York
    Posts
    1

    Re: Calculating the amount of possibilities

    Well consider the same question but with few differences:
    4 options and you have to choose 3 only and you have 3 option boxes and the same rule set where box 3 has to have the same or less number of options as box2
    box1 box2 box3
    1. 3 0 0
    2. 2 1 0
    3. 1 1 1

    Now then. Lets call the 4 options a,b,c, and d. Scenario 1 would have 4C3 possibilites only which is 4(there are 4 ways to choose 3 options I am assuming the order in these boxes do not matter)
    Option 2 would have 4C2*2C1 possibilities which is 12(The theory here is that you choose 2 in the first box and then from the remaining two you have only one option to choose from)
    ab c
    ab d
    ac b
    ac d
    and so on...
    Now the final one to consider would be each box has one option. Which would be 4C1*3C1*2C1. This is my first post by the way so sorry if this is confusing.
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