Intact triples after removing six blocks

Fifteen blocks form 5 distinct sets of 3 blocks each. Six of the 15 blocks are removed uniformly at random. What is the expected number of sets that still have all three blocks?

$12/13$. A particular set survives if all 6 removed blocks come from the other 12, probability $\binom{12}{6}/\binom{15}{6}=\tfrac{12}{65}$. By linearity, the expected number of surviving sets is $5\cdot\tfrac{12}{65}=\tfrac{12}{13}$.