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. $Noneofthese$

Answer 1

Answer: (B)

$110$

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 (undersirable)

subtract it from total ways.

$\therefore$ Desired ways $=2\times \frac{6!}{3!\times 2!}-\frac{5!}{31\times 2!}=110$