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How many different 4-digit numbers can be formed using the digits $1, 2, 3, 4, 5$ without repetition?
A$24$
B$120$
C$20$
D$625$
Answer & Solution
Correct answer: B. $120$
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.
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