Hey guys can you check to see if my answer is correct? Thanks!!

Question:

Use inclusion-exclusion to find the number of solutions in the non-negative integers to

.... with the conditions ,

My Answer:

Step 1: Find solutions with no conditions first.

Step 2: Get solutions for less than conditions

Condition 1:

Let:

So:

Therefore Solutions:

THEREFORE FINAL SOLUTION

Is this correct? thanks