Sure. I didn't post it because I didn't want someone to look at my reasoning and make a bias decision on the outcome of the answer

**Case 1**: If the first letter is A to D

1. Choose the first letter, A to D .... 4 ways

2. Choose a second letter .... 25 ways (A-D cannot be used)

3. Choose a third letter .... 24 ways (A-D + second letter cannot be used)

**Case 2**:If the the first letter is E

1. Choose the first letter to be E ... 1 way

2. Choose the second letter to be between A-F ... 5 ways (cannot pick E)

3. Choose a third letter ... 24 ways (cannot pick E or second letter)

**Case 3**:If the first letter is E and the second letter is G

1. Choose the first letter to be E ... 1 way

2. Choose the second letter to be G ... 1 way

3. Choose the third letter to be between A-F ... 5 ways (cannot pick E)

Adding together all 3 cases I get (4x25x24) + (5x24) + (5) = 2525

EDIT: Also I would be thankful if anyone could help me on my related

post.