To determine how many 3-letter code words can be formed using the first 8 letters of the alphabet (A, B, C, D, E, F, G, H), where the first letter must be a vowel, follow these steps:

Step 1: Identify the available letters.

The first 8 letters of the alphabet are: $A, B, C, D, E, F, G, H$ Among these, the vowels are A and E.

Step 2: Set restrictions for each position.

• The first letter must be a vowel, and there are 2 vowels (A, E) available.
• The second letter can be any of the 8 letters (A, B, C, D, E, F, G, H).
• The third letter can also be any of the 8 letters.

Step 3: Calculate the total number of code words.

• For the first letter, there are 2 choices (A or E).
• For the second letter, there are 8 choices (any letter from A to H).
• For the third letter, there are also 8 choices.

Therefore, the total number of 3-letter code words is calculated by multiplying the number of choices for each position: $2 \times 8 \times 8 = 128$

Final Answer:

There are 128 possible 3-letter code words.

Would you like more details or have any questions?

Here are some related questions:

1. How many 3-letter code words can be made if no letter is repeated?
2. How many 3-letter code words can be made if all letters must be vowels?
3. What if the first and third letters must be vowels?
4. How many 3-letter code words can be formed if all letters must be consonants?
5. What if the second letter must also be a vowel?

Tip: Break complex counting problems into manageable parts by analyzing restrictions for each position in sequence.