Question

How many five digits numbers can be formed using the digits $0,1,2,3$ and $5$ which are divisible by $5$ without repetition of the digits?

Answer 1

When the unit digit of a number is either $0$ or $5$ then the whole number is divisible by $5$

(i) when unit digit of a number is $5$ then,

The number of five digited numbers can be formed by using the digits $0,1,2,3,5$ without repetition of the digits $=\left(3\right)\left(3\right)\left(2\right)\left(1\right)=18$

(ii) when unit digit of a number is $0$ then,

The number of five digited numbers can be formed by using the digits $0,1,2,3,5$ without repetition of the digits $=\left(4\right)\left(3\right)\left(2\right)\left(1\right)=24$

$\therefore$ Total numbers $=18+24=42$ (Ans)