Permutations & Combinations
4-digit Numbers in Range, Divisible by 3 — With Repetition
nta_pyq_2026_jan
Grade 11
Question:
The number of numbers greater than 5000, less than 9000 and divisible by 3, that can be formed using the digits $0,1,2,5,9$, if the repetition of the digits is allowed, is _____.
Step-by-Step Solution
Key Concept: 4-digit numbers from 5001 to 8999, divisible by 3, using $\{0,1,2,5,9\}$ with repetition. Leading digit must be 5 (since 6,7,8 not available and 9000 excluded). Enumerate by digit sum $\equiv0\pmod3$.
42 numbers.
Correct Answer: 42