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giovkast

  • 2 years ago

determine the number of solutions for x part natural numbers

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  1. giovkast
    • 2 years ago
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    \[{x1}, ...., {x6} = 15\]

  2. giovkast
    • 2 years ago
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    \[\left(\begin{matrix}15 + 6 - 1 \\ 15\end{matrix}\right)\] is this the answer?

  3. RadEn
    • 2 years ago
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    what kind operations there, add, subtrac, or multiplication or division ?

  4. RadEn
    • 2 years ago
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    is it like a+b+c+d+e+f=15 ? with a,b,c,d,e, and f are natural numbers

  5. RadEn
    • 2 years ago
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    hello ?

  6. giovkast
    • 2 years ago
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    discrete math, ow sorry its addition

  7. RadEn
    • 2 years ago
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    hehe... i have guessed actually, i will use the formula : |dw:1355741391689:dw|

  8. RadEn
    • 2 years ago
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    sorry if im wrong...

  9. giovkast
    • 2 years ago
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    why did you use (15 - 1)?

  10. RadEn
    • 2 years ago
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    wait... looks i have mistaken

  11. giovkast
    • 2 years ago
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    what did you do wrong then, exactly?

  12. RadEn
    • 2 years ago
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    ok, for the first... i have mistaken after i do some experiments, it shoulde be |dw:1355743741310:dw|

  13. RadEn
    • 2 years ago
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    let's discuss for simple example below : a+b+c=6, for a,b,c are natural numbers. # if a=1, then b+c=5 or c=5-b to get c be integer , so satisfied for b=1,2,3,4 (there are 4 ways) # if a = 2, then b+c=4, or c=4-b to get c be integer , so satisfied for b=1,2,3, (there are 3 ways) # if a = 3, then b+c=3, or c=2-b to get c be integer , so satisfied for b=1,2, (there are 2 ways) # if a = 4, then b+c=2, satisfied just for b=1 and c=1 ( 1 way) so, the total ways = 4+3+2+1 = 10 it just similar by C(6-1, 3-1) = C(5,2) = 10

  14. giovkast
    • 2 years ago
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    there are 6 x's, from x1 till x6 and together they add up to 15

  15. RadEn
    • 2 years ago
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    with same idea, if given the problem : a+b+c+d=8 so, the total ways = C(8-1,4-1) = C(7,3) = 35 ways btw, i have done it by manual also like the first ^ (the answer is same)

  16. RadEn
    • 2 years ago
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    yeah, like i said before it will be C(15-1,6-1) = C(14,5) = 14!/(9!5!) = ....

  17. RadEn
    • 2 years ago
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    but, this method will be different, if a,b,c,d,... are the whole numbers :) thanks for ur question, i become more knowing for this problems ......

  18. giovkast
    • 2 years ago
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    thank you very much for the explanation

  19. RadEn
    • 2 years ago
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    you're welcome :)

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