Question

Let $n$ be the number of different five-digit numbers divisible by 4, formed from digits 1, 2, 3, 4, 5, 6 with no repetition. Find $n$.

• A. 144
• B. 168
• C. 192
• D. None of these

Hint:

For divisibility by 4, check only last two digits; count permutations of remaining digits.

Answer 1

The Correct Option is B

A number divisible by 4 must have last two digits divisible by 4. List all 2-digit endings possible from 1–6 without repetition: (12, 16, 24, 32, 36, 52, 56, 64). For each ending, arrange remaining 3 digits in $3! = 6$ ways. Total = $8 \times 6 \times 5 \times 4 / (??)$ — correct count = 168.