(i) When digits are repeated :
In a 4-digit number greater than 5000, thousandth place can be filled up by either 5 or 7
So thousandth place can be filled in 2 ways.
Since the digits can be repeated, therefore the remaining three places can be filled in 53 = 125 ways.
∴ Total number of numbers formed = 2 × 125 = 250.
But in 250 numbers, 5000 is also included.
So, total number of numbers greater than 5000 = 250 – 1 = 249
A number is divisible by 5 if the digit at unit place is either 0 or 5.
For a 4-digit number greater than 5000 and divisible by 5, the unit and thousandth place can be filled in 4 ways.
The hundredth and tenth place are to be filled in 52 = 25 ways.
∴ Number of numbers formed = 4 × 25 = 100.
Also, in 100 numbers, 5000 is included.
So, total number of numbers greater than 5000 and divisible by 5 = 100 – 1 = 99
Thus required probability =

99

249

=

33

83

(ii) When digits are not repeated :
In a 4-digit number greater than 5000, thousandth place can be filled up by either 5 or 7.
So, the hundredth, tenth and unit place may be filled in 4 × 3 × 2 = 24 ways.
∴ Total number of exhaustive cases = 2 × 24 = 48.
A number greater than 5000 and is divisible by 5 when unit place is either 0 or 5 and thousandth place is either 5 or 7.
The unit and thousandth place can be filled in 3 ways.
The tenth and hundredth place can be filled in 3 × 2 = 6 ways.
Number of favourable cases = 3 × 6 = 18.
Thus, required probability =

18

48

=

3

8