How many three-letter "codes" can be made from the following 10 letters "FGHIJKLMNO" if repetition of letters is not allowed?

To determine how many three-letter "codes" can be made from the letters "FGHIJKLMNO" without repetition, follow these steps:

1. **Count the number of available letters**:  
   The letters available are "FGHIJKLMNO", which gives us a total of 10 distinct letters.

2. **Determine the number of choices for each position in the code**:
   - For the first position, you can choose any of the 10 letters.
   - For the second position, since repetition is not allowed, you have 9 remaining letters to choose from.
   - For the third position, you have 8 remaining letters to choose from.

3. **Calculate the total number of possible codes**:  
   Multiply the number of choices for each position:
   \[
   10 \times 9 \times 8 = 720
   \]

So, there are **720** different three-letter codes possible when repetition is not allowed.

Would you like more details or have any questions?

Here are some related questions you might find interesting:
1. How many four-letter codes can be made if repetition is not allowed?
2. What if only vowels are allowed in the code, and repetition is not allowed?
3. How many three-letter codes can be made if the first letter must be a consonant?
4. How many three-letter codes can be made if exactly two letters must be the same?
5. How does the total number change if you allow repetition for only the last letter?

**Tip:** When repetition is not allowed, the number of choices decreases with each position, making the calculation a simple product of descending numbers.

Discover how many unique three-letter codes can be generated from the letters 'FGHIJKLMNO' without repetition. Follow a step-by-step calculation using combinatorial principles and the permutation formula. Ideal for high school students and anyone interested in combinatorial mathematics.

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