Final answer:
To find the number of two-letter passwords without repetition from eight letters, calculate the permutation P(8, 2), which equals 8 × 7, giving 56 different passwords.
Step-by-step explanation:
The question asks how many different two-letter passwords can be formed from the letters 'abcdefng' when repetition of letters is not allowed. To solve this, we use the concept of permutations where order matters. For the first letter of the password, there are 8 possible choices (since there are 8 unique letters to choose from). After choosing the first letter, only 7 letters are left for the second position because repetition is not allowed. Therefore, the number of possible two-letter passwords can be calculated by multiplying the possibilities for the first and second letter, which is 8 × 7.
The formula to calculate this is simply P(n, r) = n! / (n-r)! where 'n' is the total number of items to choose from, 'r' is the number of items to pick, '!' denotes factorial, and 'P' stands for permutation. So for two-letter passwords from eight distinct letters without repetition, it would be P(8, 2) = 8! / (8-2)! = 8 × 7 = 56. Hence, there are 56 different two-letter passwords that can be formed.