Q. Three letters are written to there different persons and addresses on the three envelopes are also written. Without looking at the addresses, the letters are kept in these envelopes. The probability that all the letters are not placed into their right envelopes is
A) $\frac{1}{2}$
B) $\frac{1}{3}$
C) $\frac{1}{6}$
D) $\frac{5}{6}$
Explanation
(b)
Favourable ways $= 3!\left( \ 1 - \frac{1}{1!} + \frac{1}{2!} - \frac{1}{3!} \right) = 2$
Total ways $= 3!$
$\therefore$ Probability $= \frac{2}{3!} = \frac{1}{3}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.