Even numbers from given digits — Aptitude Question
Even numbers from given digits: How many three-digit even numbers with distinct digits can be formed from 1, 2, 3,… Answer and worked solution on CodeKairo.
- Topic: Permutations & Combinations
- Section: Quantitative Aptitude
- Difficulty: Medium
- Time target: 75 seconds
Question
How many three-digit even numbers with distinct digits can be formed from 1, 2, 3, 4, 5?
Options
- 12
- 18
- 24
- 36
Show the answer and the worked solution
Correct answer: C. 24
Worked solution
- Units digit: 2 choices (2 or 4).
- Hundreds digit: 4 remaining choices; tens digit: 3 remaining.
- Total = 2 × 4 × 3 = 24.
Answer: 24.
The idea
Fix the constrained position (the units digit) first, then count the free positions. No zero is present, so the leading digit needs no special care.
Shortcut. Of the 5 × 4 × 3 = 60 three-digit numbers, each of the 5 digits ends an equal share, and 2 of them are even: 60 × 2/5 = 24.
Common trap. "36" — counting the odd units digits (1, 3, 5) instead of the even ones: 3 × 4 × 3 = 36 is the number of odd numbers.
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