$\begin{array}{1 1}(A)\;\large\frac{3}{8}\\(B)\;\large\frac{3}{5}\\(C)\;\large\frac{4}{7}\\(D)\;\large\frac{7}{8}\end{array} $

- Required probability=$\large\frac{n(E)}{n(S)}$

Step 1:

4 digit number greater than 5000 are to be formed

Digits -0,1,3,5,7

Number to be divisible by 5

$\therefore$ A number can be divisible by 5 only when its units digit is 0,5

Step 2:

Since the number have to be greater than 5000.The thousand place will be 5 or 7 and the rest three digits will have options of 4,3,2 outcomes respectively.

$\therefore$ Total number of outcomes n(S)=24+24=48

Step 3:

Number of favorable outcomes :

For a number to be divisible by 5.The unit digit should be 0 or 5.The unit digit should be 0 or 5 and thousands digits are 5 or 7.

$\therefore$ Options for tens and hundreth digits are 3 and 2.

$\therefore$ Favorable outcomes n(E)=6+6+6=18

Step 4:

$\therefore$ Required probability =$\large\frac{n(E)}{n(S)}$

$\Rightarrow \large\frac{18}{48}$

$\Rightarrow \large\frac{3}{8}$

Hence (A) is the correct answer.

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