Permutations & Combinations
Counting numbers with digit repetition and divisibility
nta_pyq_2023_jan
Grade 11
Question:
Number of 4-digit numbers (the repetition of digits is allowed) which are made using the digits 1, 2, 3 and 5, and are divisible by 15, is equal to _____
Step-by-Step Solution
Key Concept: Divisible by 15 means divisible by both 3 and 5. Units digit must be 5. Sum of all digits divisible by 3.
Units digit = 5. Remaining 3 digits from {1,2,3,5} with repetition such that total sum divisible by 3. Possible combinations yield 21 total numbers.
Correct Answer: 21