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Math Help - How many ways

  1. #1
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    How many ways

    Hi. I have 8 similar cars which I must divide/share among 12 persons.
    How many ways can the cars be divided/shared?


    I think this is: n over k And is should go like this;


    12!
    8!
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  2. #2
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    Re: How many ways

    Quote Originally Posted by stevetall View Post
    Hi. I have 8 similar cars which I must divide/share among 12 persons.
    How many ways can the cars be divided/shared?


    I think this is: n over k And is should go like this;


    12!
    8!
    That question is too vague.
    What does similar mean in this context.
    Do you mean for this purpose they can be considered identical?

    What about occupancy?
    Do you mean that only eight of the people get a car?
    Or do you mean all twelve must be assigned a car?
    Can a car not be assigned?
    Do cars have a maximum number of seats?

    Please try to write a clearer question?
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  3. #3
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    Re: How many ways

    Hi. I have 8 same cars which I must share among 12 persons.
    There are no limitations, for example I can share all the 8 cars to one person or
    four cars to one person, 3 cars to one person and 1 car to one person.
    1-8 person can get a car. 9 - 12 person cannot be assigned a car, because there are 8 cars.
    Car must always be assigned.
    Car seats don't matter.

    How many ways there are that the 8 cars be divided among 12 persons?

    So I think;

    n over k. But could it be 12! over 8!?

    12!
    8!
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  4. #4
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    Re: How many ways

    Quote Originally Posted by stevetall View Post
    Hi. I have 8 same cars which I must share among 12 persons.
    There are no limitations, for example I can share all the 8 cars to one person or four cars to one person, 3 cars to one person and 1 car to one person.
    The number of ways to put N identical objects into K different cells is
    \binom{N+K-1}{N}=\frac{(N+K-1)!}{N!\cdot (K-1)!}
    In this case N=8~\&~K=12.
    Last edited by Plato; September 23rd 2011 at 07:58 AM.
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  5. #5
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    Re: How many ways

    Thank you. I got this:


    ( 12 + 8 - 1)!
    _____________

    12! * ( 8 - 1 )!


    = 19!
    ____

    12! * 7!


    = 121645100408832000
    _______________________

    479001600 * 5040


    = 50388
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