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# Without repetition of the numbers,four digit numbers are formed with the numbers 0,2,3,5.The probability of such a number divisible by 5 is

$\begin{array}{1 1}(A)\;\large\frac{1}{5}\\(B)\;\large\frac{4}{5}\\(C)\;\large\frac{1}{30}\\(D)\;\large\frac{5}{9}\end{array}$

Step 1:
Given four digit numbers are to be formed.
$\therefore$ The numbers can't be formed starting with zero.
$\therefore$ Total numbers formed
Starting with 2=3!=6
Starting with 3=3!=6
Starting with 5=3!=6
$\therefore$ total =6+6+6=18
Step 2:
The numbers being divisible with 5,have to end with 0 or 5
$\therefore$ Total such numbers =4+4+2=10
$\therefore$ Required probability =$\large\frac{10}{18}=\frac{5}{9}$
Hence (D) is the correct option.