How many 3-letter code words are possible using the first 8 letters of the alphabet if there first letter must be a vowel

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.

How many 3-letter code words are possible using the first 8 letters of the alphabet if the first letter must be a vowel?

Explore how to determine the number of 3-letter code words that can be formed using the first 8 letters of the alphabet, with the first letter restricted to a vowel. This problem involves combinatorics and the multiplication principle of counting, making it suitable for students in Grades 6-8.

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