Combinatorics question with unequality and different subscript

a) ${x}_{1}+{x}_{2}+...+{x}_{7}\le 30$ where ${x}_{i}^{\prime}s$ are even non-negative integers.

b) ${x}_{1}+{x}_{2}+...+{x}_{7}\le 30$ where ${x}_{i}^{\prime}s$ are odd non-negative integers.

c) ${x}_{1}+{x}_{2}+...+{x}_{6}\le 30$ where ${x}_{i}^{\prime}s$ are odd non-negative integers.

These questions is from my textbook. I know to solve similar questions such that ${x}_{1}+{x}_{2}+...+{x}_{k}\le n$ where ${x}_{i}^{\prime}s$ are non-negative integers. We add an extra term on the lefthandside and the rest found by combination with repetition such that $(}\genfrac{}{}{0ex}{}{n+(k+1)-1}{n}{\textstyle )$. However , what happens when they are even or odd , is there any special technique ? Moreover , as you see the part a and b differ from only subscripts , i think that there must be a reason behind different subscript in same question.Is there any reason ? Thanks in advance..

a) ${x}_{1}+{x}_{2}+...+{x}_{7}\le 30$ where ${x}_{i}^{\prime}s$ are even non-negative integers.

b) ${x}_{1}+{x}_{2}+...+{x}_{7}\le 30$ where ${x}_{i}^{\prime}s$ are odd non-negative integers.

c) ${x}_{1}+{x}_{2}+...+{x}_{6}\le 30$ where ${x}_{i}^{\prime}s$ are odd non-negative integers.

These questions is from my textbook. I know to solve similar questions such that ${x}_{1}+{x}_{2}+...+{x}_{k}\le n$ where ${x}_{i}^{\prime}s$ are non-negative integers. We add an extra term on the lefthandside and the rest found by combination with repetition such that $(}\genfrac{}{}{0ex}{}{n+(k+1)-1}{n}{\textstyle )$. However , what happens when they are even or odd , is there any special technique ? Moreover , as you see the part a and b differ from only subscripts , i think that there must be a reason behind different subscript in same question.Is there any reason ? Thanks in advance..