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?
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?
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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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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