Final answer:
The number of password combinations using 26 letters depends on the length of the password. A one-letter password has 26 combinations, a two-letter password has 676 combinations, and a four-letter password has 456976 combinations.
Step-by-step explanation:
The student's question is about the number of password combinations possible using 26 letters. The key to solving this password combination problem is understanding the concept of permutations and combinations. When creating a password with letters, assuming each letter can only be used once, the number of possible combinations will depend on the length of the password.
If the password is one letter long, there are 26 possible combinations (one for each letter of the alphabet). If the password is two letters long, the number of combinations is the number of possibilities for the first character (26) multiplied by the number of possibilities for the second character (which would also be 26), resulting in 26 × 26 = 676 possible combinations.
However, the question does not specify the length of the password. Thus, without this information, an exact answer cannot be determined. A single letter as a password has 26 possibilities. A two-letter password has 26 to the power of 2, or 676 combinations, as mentioned. For longer passwords, you continue multiplying by 26 for each additional character.
To demonstrate, a five-letter password would have 26^5 (or 11,881,376) combinations. The options provided (26, 52, 676, 456976) suggest that the intended password lengths could be one, two, or four letters long, respectively.
So, depending on the intended length of the password, the correct number of combinations from the options given would be: If the exercise's context refers to one of these password lengths, then the student should select the corresponding answer based on that length.