total number of integral solutions for x*y*z=6! are?
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Well, if x+y+z = 40 then (x-1) + (y-1) + (z-1) = 37.
Set a=(x-1), b=(y-1), and c=(z-1). Then a+b+c=37.
So the number of solutions to the first equation where x,y,z cannot be zero is the same as the number of solutions to the second equation were a,b,c can be zero.
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