A 9-person committee has 4 B.Tech,3 M.Tech,2 PhD students. Remove3 uniformly at random. Find probability exactly2 share a category and the third is from another, to three decimals.
Count by the repeated category: $\binom42(5)+\binom32(6)+\binom22(7)=30+18+7=55$. Total triples=$\binom93=84$. Probability=55/84=.654762,or **.655**. All-three-same and one-from-each triples are excluded.
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