Permutations & Combinations
3-digit Numbers Divisible by 3 with Repetition from {1,3,5,8}
nta_pyq_2023_apr
Grade 11
Question:
Total 3-digit numbers divisible by 3 from $\{1,3,5,8\}$ with repetition is
Step-by-Step Solution
Key Concept: Digit sum divisible by 3. With digits from $\{1,3,5,8\}$ (mod 3: $1,0,2,2$). Count triples $(a,b,c)$ with $a+b+c\equiv0\pmod3$ from the 4 digits with repetition.
22 numbers.
Correct Answer: 3