Question

A management institute has $6$ senior professors and $4$ junior professors. $3$ professors are selected at random for a government project. The probability that at least one of the junior professors would get selected is:

Accepted Answer

C. 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 $= 1 - \frac{1}{6} = \frac{5}{6}$.

Selection probability

Explanation

Practise this under exam conditions