Question

A five-digits number divisible by $6$ is to be formed by using $0,1,2,3,4$ and $5$ without repetition. The number of ways in which this can be done is

• A. $60$
• B. $48$
• C. $108$
• D. $216$

Answer 1

The correct option is C $108$

(i) with out $0$ and last digit either $2$ or $4$ is $2\times 4!=48$

(ii) with $0$ as last digit and without $3$, the number as $4!=24$

(ii) with $2$ or $4$ as last digit and without $3$ number are $36$

$\therefore$ Total no. of ways $=108$