MathDB

Set

S

contains exactly

36

elements in the form of

2^m \cdot 5^n

for integers

0 \le m,n \le 5

. Two distinct elements of

S

are randomly chosen. Given that the probability that their product is divisible by

10^7

a/b

, where

a

and

b

are relatively prime positive integers, find

a +b

.
Proposed by Ada Tsui

Problem Statement