Three-digit numbers from 0 to 5 — Aptitude Question
Three-digit numbers from 0 to 5: How many three-digit numbers with distinct digits can be formed using the digits… Answer and worked solution on CodeKairo.
- Topic: Permutations & Combinations
- Section: Quantitative Aptitude
- Difficulty: Hard
- Time target: 90 seconds
Question
How many three-digit numbers with distinct digits can be formed using the digits 0, 1, 2, 3, 4, 5?
Options
- 60
- 100
- 120
- 180
Show the answer and the worked solution
Correct answer: B. 100
Worked solution
- Hundreds digit: 5 choices (not 0).
- Tens digit: 5 remaining (0 is now allowed).
- Units digit: 4 remaining.
- Total = 5 × 5 × 4 = 100.
Answer: 100.
The idea
Fill the most constrained position first — here the leading digit, which excludes zero. Ignoring that restriction gives 120, which is offered.
Shortcut. Count all ordered picks, 6 × 5 × 4 = 120, then remove those led by 0: 0 leaves 5 × 4 = 20. 120 − 20 = 100.
Common trap. "120" — treating all six digits alike, 6 × 5 × 4, and so counting strings like 012 that are really two-digit numbers.
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