Q. A committee of five is to be chosen from a group of 9 people. The probability that a certain married couple will either serve together or not at all is
A) $\frac{1}{2}$
B) $\frac{5}{9}$
C) $\frac{4}{9}$
D) $\frac{2}{3}$
Explanation
(c)
The couple server the committee in$\ ^{7}C_{3} \times \ ^{2}C_{2}$ ways. The couple does not serve the committee in$\ ^{7}C_{5}$ ways
$\therefore$Required probability$= \frac{\ ^{7}C_{3}{\times \ }^{2}C_{2} +^{7}C_{5}}{\ ^{9}C_{5}}$
$= \frac{56}{126} = \frac{4}{9}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.