Question 10
Let $\mathcal{S}$ be the set of integers between $1$ and $2^{40}$ whose binary expansions have exactly two $1$’s. If a number is chosen at random from $\mathcal{S},$ the probability that it is divisible by $9$ is $\frac{p}{q},$ where $p$ and $q$ are relatively prime positive integers. Find $p + q.$