JEE Main · MathematicsHard
How many 6-digit numbers can be formed using the digits 0, 1, 2, 3, 4, 5 such that the digits are not repeated and the number is divisible by 6?
- A.
- B.
- C.
- D.
Show correct answer & step-by-step solution
Correct answer: B —
Solution
A number is divisible by 6 if it is even and the sum of digits is divisible by 3. The sum of $0, 1, 2, 3, 4, 5$ is , which is divisible by 3, so any permutation is divisible by 3; we only need to ensure it is even and does not start with 0.
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