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Math Help - exclusion inclusion problem

  1. #1
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    exclusion inclusion problem

    q)There are 323 farms in a country that have atleast one of horses cows and sheep.if 224 have horses 85 have cows 57 have sheep and 18 farms have all three types of animals.how many farms have exactly 2 of these 3 typrs of animals?

    solution:
    A farm hve horses=224
    B farm have horses=57
    C farm have horses=18
    |AUBUC|=323
    By using inclusion exclusion principle ,we have
    |AUBUC|=|A| + |B| +|C| -|A intersection B| -|A INTERSECTION C| - |B intersection C|+|A INTERSECTION B INTERSECTION C|
    324=224 + 85 +57 +18 -|A intersection B| -|A INTERSECTION C| - |B intersection C|
    |A intersection B| +|A INTERSECTION C| + |B intersection C| =60
    which our required solution
    please tell me if i am right or wrong
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  2. #2
    Super Member
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    Athens, OH, USA
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    Re: exclusion inclusion problem

    Hi,
    Your solution looks fine to me.
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