*********** How many three-letter code words can be constructed from the first ten letters of the Greek alphabet if no repetitions are allowed? different code words Need Help? Read It
*********** How many three-letter code words can be constructed from the first ten letters of the Greek alphabet if no repetitions are allowed? different code words Need Help? Read It
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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![**Educational Exercise: Combinatorics - Greek Alphabet Code Words**
**Question:**
How many three-letter code words can be constructed from the first ten letters of the Greek alphabet if no repetitions are allowed?
---
**Instructions & Explanations:**
1. **Understanding the Problem:**
- You need to create three-letter code words.
- The letters should come from the first ten letters of the Greek alphabet.
- No letter should be repeated in a code word.
2. **Steps to Solve the Problem:**
- Let's denote the first ten Greek letters, for simplicity, as \( \alpha_1, \alpha_2, \ldots, \alpha_{10} \).
- For the first position of the three-letter code word, there are 10 possible choices.
- Once the first letter is chosen, there are 9 remaining choices for the second letter.
- After choosing the first two letters, there are 8 remaining choices for the third letter.
3. **Calculating the Total Number of Code Words:**
- The formula to calculate the total number of possible combinations without repetition is given by: \( 10 \times 9 \times 8 \).
4. **Detailed Calculation:**
\[
10 \times 9 \times 8 = 720
\]
**Answer:**
720 different three-letter code words can be constructed from the first ten letters of the Greek alphabet with no repetitions allowed.
---
**Need Help?**
[Read It]
**Work Submission:**
[ ] Show My Work (Optional)
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Transcribed Image Text:**Educational Exercise: Combinatorics - Greek Alphabet Code Words**
**Question:**
How many three-letter code words can be constructed from the first ten letters of the Greek alphabet if no repetitions are allowed?
---
**Instructions & Explanations:**
1. **Understanding the Problem:**
- You need to create three-letter code words.
- The letters should come from the first ten letters of the Greek alphabet.
- No letter should be repeated in a code word.
2. **Steps to Solve the Problem:**
- Let's denote the first ten Greek letters, for simplicity, as \( \alpha_1, \alpha_2, \ldots, \alpha_{10} \).
- For the first position of the three-letter code word, there are 10 possible choices.
- Once the first letter is chosen, there are 9 remaining choices for the second letter.
- After choosing the first two letters, there are 8 remaining choices for the third letter.
3. **Calculating the Total Number of Code Words:**
- The formula to calculate the total number of possible combinations without repetition is given by: \( 10 \times 9 \times 8 \).
4. **Detailed Calculation:**
\[
10 \times 9 \times 8 = 720
\]
**Answer:**
720 different three-letter code words can be constructed from the first ten letters of the Greek alphabet with no repetitions allowed.
---
**Need Help?**
[Read It]
**Work Submission:**
[ ] Show My Work (Optional)
[Submit Answer]
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