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Math Help - Discrete math

  1. #1
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    Discrete math

    How do i solve the following questions?



    1.How many nonnegative solutions are there to the pair of equations
    x1 + x2 + x3 = 6, x1 + x2 + x3 + x4 + x5 = 15?

    2. There is a train station in Smalltown where there are trains going north and trains going south. If there are 3 southbound trains and 4 northbound train departures in a day, how many ways are there to leave Smalltown by train?
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  2. #2
    Super Member Gamma's Avatar
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    Iowa City, IA
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    1)
    006
    015
    024
    033
    042
    051
    060
    105
    114
    123
    132
    141
    151
    204
    213
    222
    231
    242
    303
    312
    321
    330
    402
    411
    420
    501
    510
    600

    Think thats all of them for the first equation.

    So each of those works to give you 6 for the sum of the first 3 x's so now figure out how many ways to get 9 in the last 2 spots

    09
    18
    27
    36
    45
    54
    63
    72
    81
    90

    now multiply however many you got in each of these cases. That is how many solutions all together there are.
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  3. #3
    Super Member Gamma's Avatar
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    The second question doesnt make any sense. there are 7 trains leaving, so that seems to indicate 7 ways of leaving this town. There must be something else going on that is not indicated, because as it stands i do not see the significance of this question at all
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  4. #4
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    thank you

    Thank you!

    I need help with one more question involving discrete math:


    2)A hungry spider sits at one corner of a rectangular three-dimensional grid with 4 steps in every direction. In the opposite corner there is a juicy fly that cannot move. The spider can only move along the grid lines, that is right/left, up/down and front/back. Assuming that the spider in the upper left back corner is efficient and doesn't waste time on detours, in how many ways can it reach the fly in the lower right front corner?
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  5. #5
    Super Member Matt Westwood's Avatar
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    Quote Originally Posted by Hayoota View Post
    Thank you!

    I need help with one more question involving discrete math:


    2)A hungry spider sits at one corner of a rectangular three-dimensional grid with 4 steps in every direction. In the opposite corner there is a juicy fly that cannot move. The spider can only move along the grid lines, that is right/left, up/down and front/back. Assuming that the spider in the upper left back corner is efficient and doesn't waste time on detours, in how many ways can it reach the fly in the lower right front corner?
    The rules of this forum suggest that it is conventional to put new questions in a completely new thread.
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