2) A school district assigns each of their students a password that consists of three unique letters (no repetition), followed by three unique numbers (no repetition), and finally one symbol (@. , #, $, %, or 8) at the end. How many passwords are possible?

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Author:Amos Gilat
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**Password Combinatorics Problem**

**Problem Statement:**

A school district assigns each of their students a password that consists of:
- Three unique letters (no repetition)
- Three unique numbers (no repetition)
- One symbol chosen from the set {!, #, $, %, or &} at the end

**Question:** How many passwords are possible?

**Solution Explanation:**

1. **Three Unique Letters:**
   - There are 26 possible letters in the English alphabet.
   - The selection is without repetition.

2. **Three Unique Numbers:**
   - There are 10 possible digits (0-9).
   - The selection is without repetition.

3. **One Symbol:**
   - Choices are {!, #, $, %, &}.
   - There are 5 different symbols available.

To find the total number of passwords, calculate the number of ways to choose and arrange these components and multiply them together.

(Note: For educational purposes, proceed to provide detailed calculations on a separate section).
Transcribed Image Text:**Password Combinatorics Problem** **Problem Statement:** A school district assigns each of their students a password that consists of: - Three unique letters (no repetition) - Three unique numbers (no repetition) - One symbol chosen from the set {!, #, $, %, or &} at the end **Question:** How many passwords are possible? **Solution Explanation:** 1. **Three Unique Letters:** - There are 26 possible letters in the English alphabet. - The selection is without repetition. 2. **Three Unique Numbers:** - There are 10 possible digits (0-9). - The selection is without repetition. 3. **One Symbol:** - Choices are {!, #, $, %, &}. - There are 5 different symbols available. To find the total number of passwords, calculate the number of ways to choose and arrange these components and multiply them together. (Note: For educational purposes, proceed to provide detailed calculations on a separate section).
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