Final answer:
There are 512 possible three-letter code words that can be made from the letters in "COMPUTER" with repetitions permitted, utilizing the calculation of 8 to the power of 3.
Step-by-step explanation:
The number of three-letter code words that can be made using the letters in the word "COMPUTER," with repetitions permitted, can be calculated using the principles of permutations and combinations. As there are 8 unique letters in "COMPUTER," and each position in the code word can be filled by any of the 8 letters (since repetitions are allowed), the total number of three-letter code words is 8 × 8 × 8 (8 to the power of 3), which equals 512 possible code words.
To calculate this, you determine the number of choices for each position in the code word and then multiply these together. For the first letter, there are 8 possibilities, similarly for the second letter, and the same for the third letter. Thus, the calculation looks like this:
- 8 (choices for the first letter)
- 8 (choices for the second letter)
- 8 (choices for the third letter)
Which results in 8^3 or 512 unique three-letter code words.