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anonymous
 3 years ago
determine the number of solutions for x part natural numbers
anonymous
 3 years ago
determine the number of solutions for x part natural numbers

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anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0\[{x1}, ...., {x6} = 15\]

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0\[\left(\begin{matrix}15 + 6  1 \\ 15\end{matrix}\right)\] is this the answer?

RadEn
 3 years ago
Best ResponseYou've already chosen the best response.1what kind operations there, add, subtrac, or multiplication or division ?

RadEn
 3 years ago
Best ResponseYou've already chosen the best response.1is it like a+b+c+d+e+f=15 ? with a,b,c,d,e, and f are natural numbers

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0discrete math, ow sorry its addition

RadEn
 3 years ago
Best ResponseYou've already chosen the best response.1hehe... i have guessed actually, i will use the formula : dw:1355741391689:dw

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0why did you use (15  1)?

RadEn
 3 years ago
Best ResponseYou've already chosen the best response.1wait... looks i have mistaken

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0what did you do wrong then, exactly?

RadEn
 3 years ago
Best ResponseYou've already chosen the best response.1ok, for the first... i have mistaken after i do some experiments, it shoulde be dw:1355743741310:dw

RadEn
 3 years ago
Best ResponseYou've already chosen the best response.1let'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=5b 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=4b 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=2b 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(61, 31) = C(5,2) = 10

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0there are 6 x's, from x1 till x6 and together they add up to 15

RadEn
 3 years ago
Best ResponseYou've already chosen the best response.1with same idea, if given the problem : a+b+c+d=8 so, the total ways = C(81,41) = C(7,3) = 35 ways btw, i have done it by manual also like the first ^ (the answer is same)

RadEn
 3 years ago
Best ResponseYou've already chosen the best response.1yeah, like i said before it will be C(151,61) = C(14,5) = 14!/(9!5!) = ....

RadEn
 3 years ago
Best ResponseYou've already chosen the best response.1but, 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 ......

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0thank you very much for the explanation
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