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To solve this problem, we need to calculate the number of possible serial numbers consisting of 3 letters followed by 3 digits. Let's break down the calculations:

### Step 1: Choosing the letters
- The letters are chosen from the first 5 letters of the alphabet (A, B, C, D, E) with no repeats.
- The number of ways to choose 3 different letters from 5 is given by the permutation formula \( P(n, r) = \frac{n!}{(n - r)!} \), where \( n \) is the total number of items, and \( r \) is the number of items to choose.

\[
P(5, 3) = \frac{5!}{(5 - 3)!} = \frac{5 \times 4 \times 3}{1} = 60
\]

### Step 2: Choosing the digits
- The digits are chosen from the 10 digits (0-9) with no repeats.
- The number of ways to choose 3 different digits from 10 is given by \( P(10, 3) \).

\[
P(10, 3) = \frac{10!}{(10 - 3)!} = \frac{10 \times 9 \times 8}{1} = 720
\]

### Step 3: Calculating the total number of serial numbers
- Multiply the number of ways to choose the letters by the number of ways to choose the digits:

\[
60 \times 720 = 43,200
\]

Thus, a total of 43,200 unique serial numbers can be generated.

Would you like further details or have any questions?

Here are five related questions:
1. How would the solution change if repeats were allowed for the letters and digits?
2. What if the letters had to be chosen from all 26 letters of the alphabet instead of just the first five?
3. How many serial numbers could be made if the order of the letters did not matter?
4. What if the serial number format changed to two letters followed by four digits?
5. How would the solution be affected if the digits were allowed to repeat?

**Tip:** Understanding permutations and combinations is essential for counting problems in probability and combinatorics.

Serial numbers for a product are to be made using 3 letters followed by 3 digits. The letters are to be taken from the first 5 letters of the alphabet, with no repeats. The digits are taken from the 10 digits (0, 1, 2, ..., 9), with no repeats. How many serial numbers can be generated?

This page explains how to calculate the number of serial numbers that can be generated using 3 letters from the first 5 letters of the alphabet and 3 digits from 0-9, without repeats. Learn about permutations, the counting principle, and how to apply them to this problem. Suitable for Grades 9-10.

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