Question

Find the number of $5$ digit numbers using digits $0,1,2,3,4,5$ (without repetition) such that they are divisible by $5$ :

• A. $218$
• B. $150$
• C. $216$
• D. $210$

Answer 1

The correct option is C $216$

For number to be divisible $5,$ the last digit should be $0$ or $5.$
If last digit is $0,$ then total number are ${}^5{P}_4=120$
If last digit is $5,$ then total number are ${}^4{P}_3\times 4=96$
So, total numbers are $120+96=216.$