Find the number of integral solutions for the equation $x_1+ x_2 + x_3 + x_4 + x_5 + x_6 = 31$
where $x_1 ≥ 1, x_2 ≥ 2, x_3 ≥ 2, x_4 ≥ 4, x_5 ≥ 6, x_6 ≥ 5?$
I have no idea how to proceed here ? I read somewhere that this question can also be done using generating function, an approach using generating function's will be appreciated.