Sampling and Experiments · Superchallenge problem

The 25 members of a club are labelled $01$ to $25$. To choose a simple random sample of 2, a researcher reads two-digit numbers $00$ to $99$ from a table of random digits, ignoring any number that is not a label and any label already chosen, until 2 different labels are chosen. What is the expected number of two-digit numbers read?