I have to find the number of solutions to $x_1+x_2+x_3=2018$ ,
with the following conditions :
- $x_1,x_2,x_3$ are even numbers.
- $x_1$ is even while $x_2$ and $x_3$ are odd.
I guess I have to use stars and bars in order to solve it, so in case one I reffed to every two stars as one star and then solved this equation $x_1+x_2+x_3=1009$ (with stars and bars again). but in case two i'm stuck, I don't understand how to divide the stars correctly when odd and even conditions are involved.
appreciate your help very much!