Problem
COM-B1-M03-P012 Positive Solutions
#12
★★☆☆☆ Level 2 of 5
How many positive solutions does \(x+y+z=10\) have?
First subtract \(1\) from each variable.
Let \(x'=x-1\), \(y'=y-1\), \(z'=z-1\). Then \(x'+y'+z'=7\) in nonnegative variables. Answer: \(\binom{9}{2}=36\).
Positivity becomes nonnegativity.