Question

How many different numbers, which are smaller than $2\cdot {10}^3$ and are divisible by $3$, can be written by means of the digits $0,1$ and $2$ (the numbers cannot begin with $0$)?

Answer 1

The number should be less than $2000$

So the first digit must be 1

The second digit can be anything in $0,1,2$ i.e., $3$ chances

The third digit also can be anything in $0,1,2$ ie., $3$ chances

The fourth digit has only one chance to make the sum of digits divisible by 3

So finally the total number of such numbers id $3\times 3=9$