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    How many solutions do the equation have

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    Hello,

    I have a discrete math problem. It states how many solutions (X_1,...,X_6) in the Natural numbers have the equation X_1+ ... + X_6 = 10

    So the way my teacher explained it was (10,0,0,0,0,0) would be one choice, (0,10,0,0,0,0) would be another, so basically it would look like this...

    (10,0,0,0,0,0)
    (0,10,0,0,0,0)
    (0,0,10,0,0,0)
    ````````````````
    (0,0,0,0,0,10)

    THEN you have other solutions like
    (1,9,0,0,0,0)
    (0,1,9,0,0,0)
    ```````````````
    (0,0,0,0,1,9)

    And keep going until all the combinations of numbers are found.

    I see that each, i suppose you would call them sets, have 6 combinations. So like (10) has 6, (1,9) has 6, ... you could do (1,1,8), or (1,1,1,7), or whatever else combinations. I just don't understand how to determine how many combinations there are.

    Any help would be appreciated.

    -John

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    https://brainmass.com/math/discrete-math/many-solutions-equation-have-447267

    Solution Preview

    How many solutions (X_1,...,X_6) have the equation X_1+ ... + X_6 = 10
    Hello,

    I have a discrete math problem. It states how many solutions (X_1,...,X_6) in the Natural numbers have the equation X_1+ ... + X_6 = 10

    So the way my teacher explained it was (10,0,0,0,0,0) would be one choice, (0,10,0,0,0,0) would be another, so basically it would look like this...

    Dear Student
    Your problem ...

    Solution Summary

    The expert determines how many solutions do equations have.

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