N is a three digit multiple of 7.
N could be 105, 112, 119, 126…..994.
Or, 15 × 7, 16 × 7…..142 × 7.
Or there are 142–14 = 128 numbers.
Within these we need to locate the multiples of 5.
Or, we need to isolate multiples of 35.
Or, we need to see how many numbers there are in the list 105, 140, 175…..980.
35 × 3, 35 × 4…35 × 28…
Or, there are 26 such numbers.
Probability 26/128 = 13/64
Answer choice (c).
Correct Answer : 13/64