Final answer:
The number of different -letter passwords that can be formed from the letters H, I, J, K, L, and M without repetition is 720.
Step-by-step explanation:
To find the number of different -letter passwords that can be formed from the given letters H, I, J, K, L, and M without repetition, we can use the concept of permutations.
Since no repetition of letters is allowed, we have 6 options for the first letter, 5 options for the second letter, 4 options for the third letter, and so on, until we have 2 options for the second-to-last letter and 1 option for the last letter.
Therefore, the total number of different -letter passwords that can be formed is 6! = 720.