How many different 4-digit numbers can be formed using the digits $1, 2, 3, 4, 5$ without repetition?

We need to arrange 4 digits chosen from 5 distinct digits with no repetition. That's $^5 P_4$: $^5 P_4 = \dfrac{5!}{(5-4)!} = \dfrac{120}{1} = 120$. Alternative count by positions: 5 choices for the thousands digit then 4 for hundreds, then 3 for tens, then 2 for units. $5 \times 4 \times 3 \times 2 = 120$ ✓. Option B (625) would be allowed repetition: $5^4 = 625$. Option C is just $4!$ ignoring the choice of digits to use.