Permutations and Combinations
Divisibility Rules
JEE Advanced 2018 Paper 1
Grade 11
Question:
The number of 5-digit numbers which are divisible by 4, with digits from the set $\{1, 2, 3, 4, 5\}$ and repetition of digits allowed, is _____.
Step-by-Step Solution
Key Concept: Divisibility by 4: last two digits must form a 2-digit number divisible by 4. From $\{1, 2, 3, 4, 5\}$: valid endings are $12, 24, 32, 44, 52$ — that is 5 choices. First 3 digits: $5^3 = 125$ each. Total $= 5 \times 125 = 625$.
The detailed step-by-step mathematical proof is available inside the Mathbee app workspace.
Correct Answer: 625