Question

Number of numbers greater than a million and divisible by $5$ which can be formed by using only the digits $1,2,1,2,0,5\&2$ is -

• A. 120
• B. 110
• C. 90
• D. none of these

Answer 1

Answer: (B)

For a number to be divisible by $5,5$ or $0$ should be at units place.
$\therefore$ Unit place can be filled by $2$ ways
Remaining digits can be filled in $\frac{6!}{3!\times 2!}$ ways.
$\therefore$ Total ways $=\frac{2\times 6!}{3!2!}$
But these arrangements also include cases where 0 is at millions place and 5 at units place, which are undesirable cases
$\Rightarrow \frac{5!}{3!\times 2!}$ ways (undesirable)
subtract it from total ways.
$\therefore$ Desired ways $=2\frac{6!}{3!\times 2!}-\frac{5!}{3!\times 2!}=110$