Three-digit numbers with distinct digits — Aptitude Question
Three-digit numbers with distinct digits: How many three-digit numbers with all digits different can be formed… Answer and worked solution on CodeKairo.
- Topic: Permutations & Combinations
- Section: Quantitative Aptitude
- Difficulty: Easy
- Time target: 40 seconds
Question
How many three-digit numbers with all digits different can be formed using the digits 1 to 6?
Options
- 100
- 120
- 150
- 216
Show the answer and the worked solution
Correct answer: B. 120
Worked solution
- Hundreds digit: 6 choices; tens: 5 remaining; units: 4 remaining.
- 6 × 5 × 4 = 120.
Answer: 120.
The idea
Fill positions in order and multiply the choices. Watch for a zero, which cannot lead; there is none here.
Shortcut. It is ⁶P₃ = 6 × 5 × 4 = 120; 216 = 6³ would allow digits to repeat.
Common trap. 216 — 6 × 6 × 6, letting digits repeat; each place has one fewer digit to choose from.
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