Permutations & Combinations
3-Digit Numbers Not Divisible by 3
nta_pyq_2024_apr
Grade 11
Question:
The number of 3-digit numbers, formed using the digits 2, 3, 4, 5 and 7, when the repetition of digits is not allowed, and which are not divisible by 3, is equal to
Step-by-Step Solution
Key Concept: Total 3-digit numbers from $\{2,3,4,5,7\}$ without repetition: $5\times4\times3=60$. Subtract those divisible by 3 (digit sum divisible by 3). Find triplets from $\{2,3,4,5,7\}$ with sum divisible by 3.
6 valid triplets (none with sum divisible by 3) × $3!=36$ arrangements. Answer: 36.
Correct Answer: 36