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Math Help - computation

  1. #1
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    Apr 2009
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    computation

    Chinese Astrology total combinations

    12 male animals and 12 female animals = 144 combinations ???
    but I need to factor in:
    each could be born in one of 12 months
    each could be born in one of 12 hours (yes, 12)
    each could be one of five elements (earth, water, wood, metal, fire)

    Is the answer 12 x12 x 12 x 12 x 5 = 103,680
    ?????? I need help please (
    Susan
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  2. #2
    MHF Contributor
    Grandad's Avatar
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    South Coast of England
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    Combinatorics

    Hello Susan
    Quote Originally Posted by brainbaby View Post
    Chinese Astrology total combinations

    12 male animals and 12 female animals = 144 combinations ???
    but I need to factor in:
    each could be born in one of 12 months
    each could be born in one of 12 hours (yes, 12)
    each could be one of five elements (earth, water, wood, metal, fire)

    Is the answer 12 x12 x 12 x 12 x 5 = 103,680
    ?????? I need help please (
    Susan
    Welcome to Math Help Forum!

    What you've done here is to choose a pair of animals first (and you're right there are 144 ways of doing this), and then to allocate for them a month, a time and an element.

    The problem with this is that it assumes that each animal in the pair that has been chosen, has the same month, time and element. I presume that you didn't intend this (although you haven't said so), in which case you need to say:

    • The male animal can be allocated a month, time and element in 12 x12 x 5 ways.
    • The female animal can be allocated a month, time and element in 12 x 12 x 5 ways.

    So once the pair has been chosen (in 12 x 12 ways) we allocate each member of the pair its month, time and element in (12 x 12 x 5) x (12 x 12 x 5) ways.

    So the total number of choices altogether is (12 x 12) x (12 x 12 x 5) x (12 x 12 x 5) = 74 649 600

    Grandad
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  3. #3
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    Red face Thank you Grandad

    Thanks for being there.
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