How many solutions are there to the equation? ok, this one is really starting to piss me off :( ... x1 + x2 + x3 + x4 + x5 = 21, x1>=1 i tried all the formulas: n! (nr)! n!/(r!(nr)!) (n+r1)!/(r!(n1)!)  i think it's this one but nothing's working or even coming close to the answer ... i don't get it :( how do i do this? 
Re: How many solutions are there to the equation? is it not 25!/(21!*4!) = 12650? the answer is 10626, but that's the closest i can get to it :( 
Re: How many solutions are there to the equation? 24!/(20!*4!) works tho ... :? is it because x1 is >=1 and not >=0? ... 
Re: How many solutions are there to the equation? doesn't work far x_i >=2 ... so it's not 23!/(19!*4!) ... the actual answer is 1365 
Re: How many solutions are there to the equation? Let's call f(n, k) the number of solutions to x1 + ... + xn = k with xi >= 0. You're looking for f(5, 16), since this is what you get by assuming each variable has at least 1. It's clear that f(n, k) = f(n1, k) + f(n1, k1) + ... + f(n1, 0) since this is just saying that xn can have any value from 0 to k. So you have f(5, 16) = f(4, 16) + f(4, 15) + ... + f(4, 0) = f(3, 16) + 2f(3, 15) + 3f(3, 14) + ... + 17f(3, 0) = . . . You can probably solve it this way. You need to keep track of what the coefficients are at each step, but otherwise it's pretty easy. At the end you can simplify f(1, k) = 1 or f(2, k) = k + 1. 
Re: How many solutions are there to the equation? Quote:
could you please explain this a bit more? 
Re: How many solutions are there to the equation? Quote:

Re: How many solutions are there to the equation? Quote:
f(n, k) = f(n1, k) + f(n1, k1) + ... + f(n1, 0) 
Re: How many solutions are there to the equation? ok, i figured than one out and also the one for x_i >=2, i = 1,2,3,4,5 it's 215*2 = 11 (11,5) 15!/(11!*4!) but what do i do for 0 =< x1 >= 10? 
Re: How many solutions are there to the equation? Quote:
ahhh... ok... did 364+455+560+680+816+969+1140+133+1540+1771+2024 = 11649 it works ... but tried the same approach with 0 =< x1 >= 3 1 =< x4 <4 x3 >= 15 and it didn't work :( how come? 
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