Question

A law firm has nine senior and five junior partners. A committee of three partners is selected at random to represent the firm at a conference. What is the probability that at least one of the junior partners is on the committee? (round to three decimal places)

Answer 1

Required probability

$=\frac{\binom{9}{2}\binom{5}{1}}{\binom{14}{3}}+\frac{\binom{9}{1}\binom{5}{2}}{\binom{14}{3}}+\frac{\binom{9}{0}\binom{5}{3}}{\binom{14}{3}}=0.769$