Question

The number of all $5$ digited numbers which can formed by using the digits $0,1,2,3,4,5$ :no digit being repeated in any number and which are divisible by $5$ is

• A. $5!+4.4!$
• B. $5!$
• C. $4.4!$
• D. $216$

Answer 1

The correct option is D $216$

Since the no. is divisible by 5

$\therefore$ The no. should end with 5 or 0

So, 2 cases will be formed

First end with $0\Rightarrow 5\times 4\times 3\times 2=120$

Second end with $5\Rightarrow 4\times 4\times 3\times 2=96$

$\therefore Answer=120+96=216$