. Total number of outcomes = The number of ways of selecting 3 professors at random from a total of 10 professors. = 10C3 = 120 ways. Expected number of outcomes = Selecting 3 professors so that at least one of the junior professor is selected. The possible cases are, Case(1): Selecting 1 junior professor out of 4 and Selecting 2 senior professor out of 6 =4C1×6C2. Case(2): Selecting 2 junior professor out of 4 and Selecting 1 senior professor out of 6 =4C2×6C1. Case (3): Selecting 3 junior professor out of 4 =4C3. So Expected number of outcomes = 4C1×6C2+4C2×6C1+4C3=4×15×6×6+4 = 100 ways. Probability =