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Math Help - Possibilities in a given set

  1. #1
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    Possibilities in a given set

    There are 3 men A,B and C. They have 4 sons in total.
    What are the total possibilities of the order of no. of sons they have.
    How do we find it.
    Plz help I am totally new to this topic.
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  2. #2
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    Re: Possibilities in a given set

    Quote Originally Posted by AaPa View Post
    There are 3 men A,B and C. They have 4 sons in total.
    What are the total possibilities of the order of no. of sons they have.
    How do we find it.
    Solve A+B+C=4 in the non-negative integers.
    We can put N identical objects into K different cells in
    \binom{N+K-1}{N} ways.
    Here which is which?
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  3. #3
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    Re: Possibilities in a given set

    Quote Originally Posted by Plato View Post
    \binom{N+K-1}{N} ways.
    I don't understand this. I am not being taught this anywhere.
    It just came to my mind randomly.
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    Re: Possibilities in a given set

    Quote Originally Posted by AaPa View Post
    I don't understand this. I am not being taught this anywhere.
    It just came to my mind randomly.
    Well then make a list:
    400
    310
    301
    220
    etc
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  5. #5
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    Re: Possibilities in a given set

    But I wanted to do it using a formula.
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  6. #6
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    Re: Possibilities in a given set

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  7. #7
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    Re: Possibilities in a given set

    thanks a lot.
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  8. #8
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    Re: Possibilities in a given set

    N=4 sons (1234) to separate into K=3 groups, using K-1=2 dividers (--).
    So 123-4- means 3,1,0
    So 1-23-4 means 1,2,1
    So we have to choose K-1=2 dividers among N+K-1=4+2=6 symbols,
    so #ways is (6 over 2), or (4+3-1 over 2), or (N+K-1 over K-1), or (N+K-1 over N)
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  9. #9
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    Re: Possibilities in a given set

    Ya; and to "see them" as Plato suggested, just write 'em down in ascending order:
    004
    013
    022
    031
    040....5
    103
    112
    121
    130....4
    202
    211
    220....3
    301
    310....2
    400....1
    .........15
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