Problem
COM-B1-M03-P019 Distribution with Minimums
#19
★★★☆☆ Level 3 of 5
How many nonnegative integer solutions does \(x+y+z=12\) have if \(x\ge2\), \(y\ge3\)?
Set \(x'=x-2\), \(y'=y-3\).
Let \(x'=x-2\), \(y'=y-3\). Then \(x'+y'+z=7\), all variables nonnegative. The number of solutions is \(\binom{9}{2}=36\).
Lower bounds become shifts.