Permutations & Combinations
Counting multi-digit numbers with divisibility using limited digits
nta_pyq_2023_jan
Grade 11
Question:
The total number of six digit numbers, formed using the digits 4, 5, 9 only and divisible by 6, is _____.
Step-by-Step Solution
Key Concept: Divisible by 6 means divisible by both 2 and 3. Since digits 4,5,9 are all odd except 4, last digit must be 4. Sum of digits must be divisible by 3.
Last digit=4. Remaining 5 digits from {4,5,9} with repetition. Total sum must be divisible by 3. Systematically counting gives: single digit type, two-digit type, three-digit type combinations summing to 81 total.
Correct Answer: 81