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Math Help - combination 2

  1. #1
    Senior Member
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    combination 2

    4 men and their wives , 4 bachelors and 4 spinsters are travelling in two 8-seater compartments of a train , one of which is a smoking compartment while the other is not . In how many ways can the party be split up if no wife is separated from her husband ?
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  2. #2
    Member
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    Mumbai
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    I'm not sure about the method, but here goes:

    Pair up each husband and wife as a "couple". So we have 4 couples, 4 bachelors and 4 spinsters.

    Effectively we have 12 "seats"

    Now, let's take the following cases.


    1. All couples in one compartment .
    No. of ways this can be achieved is 2

    2. Three couples in one compartment,

    No. of combinations = =224

    3. Two couples in one compartment

    No. of combinations = =840

    4. One couple in one compartment

    No. of combinations = =224


    Total combinations = 1. +2. +3. + 4. = 450+840 = 1290?
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