One ticket is selected at random from 50 tickets numbered 00, 01, 02, …., 49.

(d) : Any number in the set
S = {00, 01, 02, ...., 49} is of the form ab where 

a ∈ {0, 1, 2, 3, 4} and b ∈ {0, 1, 2, ..., 9} for the product of digits to be zero, the number must be of the form either x0 which are 5 in numbers, because 

x ∈{0, 1, 2, 3, 4}  

or of the form 0x which are 10 in numbers because
x ∈ {0, 1, 2, ..., 9}
The only number common to both = 00
Thus the number of numbers in S, the product of whose digits is zero = 10 + 5 – 1 = 14 Of these the number whose sum of digits is 8 is just one, i.e. 08
The required probability = 1/14.