Final answer:
There can be 720 different passwords made using the letters A, B, C, D, E, and F, with each letter only being used once.
Step-by-step explanation:
The question asks how many passwords can be made using the letters A, B, C, D, E, F, with each letter being used only once. To solve this, you would use factorial notation, because the arrangement of the letters matters, making it a permutations problem. Since there are six letters, you would use 6! (six-factorial), which is calculated as 6×5×4×3×2×1.
Doing the calculation:
- 6 × 5 = 30
- 30 × 4 = 120
- 120 × 3 = 360
- 360 × 2 = 720
- 720 × 1 = 720
Therefore, there are 720 different passwords that can be made when using each letter only once.