Provide full explanation with other examples if it possible

Consider the set X = {A,B, C, D,E, F, G} case 1 How many 4-letter lists from X (with repetition not allowed) are there that don't start with A or E, or do end with G? I'm confused here should the answer be 4*6*5*1 Or the answer is 4*5*4*1 Please explain which one is right and why the other one is wrong? Case 2 How many 4-letter lists from X (with repetition not allowed) are there that don't start with A or E, and do end with A or G? also what is the difference in this case how the answer gone change