Final answer:
The total number of different 4-letter sequences that can be formed using the first nine letters of the alphabet, with repetition allowed, is 9 raised to the power of 4, which is 6561 different sequences.
Step-by-step explanation:
The student is asking how many different 4-letter sequences can be created using the first nine letters of the English alphabet (A, B, C, D, E, F, G, H, I) with the possibility of letter repetition. To calculate this, we consider each of the four positions in the sequence separately. Since repetition is allowed, each position can be filled by any of the nine available letters.
For the first position, there are 9 possibilities (A, B, C, D, E, F, G, H, I). The second position also has 9 possibilities, and this pattern continues for the third and fourth positions as well. Therefore, the number of different sequences that can be formed is 9 (for the first letter) times 9 (for the second letter) times 9 (for the third letter) times 9 (for the fourth letter), which equals 94 or 6561 different 4-letter sequences.
The calculation directly scales from the four nucleotide base letters of RNA, where the number of genetic code words possible from the four nucleotide bases (A, U, G, C) is 43 (since there are three nucleotide bases in a genetic code word, as opposed to four in our letter sequence problem). As such, an analogous strategy is applied when considering letter sequences, where we raise the number of options per position to the power corresponding to the number of positions in the sequence.