Selection probability

Total professors $= 10$. Total ways to choose 3 professors $= \binom{10}{3} = 120$.

Probability of selecting no junior professor (selecting all 3 from 6 senior professors) $= \frac{\binom{6}{3}}{\binom{10}{3}} = \frac{20}{120} = \frac{1}{6}$.

Probability that at least one junior professor is selected $= 1 - \frac{1}{6} = \frac{5}{6}$.