How many three-letter "codes" can be made from the following letters "FGHIJKLMNO" if repetition of letters is allowed?

To solve the problem of determining how many three-letter "codes" can be made from the letters "FGHIJKLMNO" with repetition allowed, we can 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**:  
   Since repetition is allowed, each of the three positions in the code can be filled by any of the 10 letters.

3. **Calculate the total number of possible codes**:  
   Since there are 10 choices for the first letter, 10 choices for the second letter, and 10 choices for the third letter, the total number of codes can be calculated as:
   \[
   10 \times 10 \times 10 = 10^3 = 1000
   \]

So, there are **1,000** different three-letter codes possible.

Would you like further details or have any questions?

Here are some related questions you might find interesting:
1. How many three-letter codes can be made if repetition is not allowed?
2. What if only vowels are allowed in the code, how many such codes can be made?
3. How many four-letter codes can be made with repetition allowed?
4. What if you are restricted to using only odd-indexed letters (e.g., F, H, J, L, N)?
5. How does the number of codes change if only two-letter codes are made?

**Tip:** When dealing with permutations where repetition is allowed, the total number of combinations is found by raising the number of available items to the power of the number of positions.

Discover how many three-letter codes can be made from the letters FGHIJKLMNO with repetition allowed. Follow a step-by-step explanation using permutations with repetition formula. Suitable for students in Grades 6-8.

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