Question

Total number of $4$ digit numbers that can be formed using digits $0,1,3,4,7$ without repetition such that it should be a multiple of $6$ are

• A. $18$
• B. $16$
• C. $10$
• D. $12$

Answer 1

The correct option is B $16$

The digit in the unit's place could be either $4$ or $0$
When the unit place is occupied with $4$ then the other set of numbers possible could be $(1,3,7)$ or $(0,1,7)$

total numbers will be $3\times 2\times 1+2\times 2\times 1=10$

When the unit place is occupied with $0$ then the other set of numbers possible could be $(1,4,7)$

total numbers will be $3\times 2\times 1=6$

total required numbers are$=10+6=16$