Question

Three letters are written to three different persons and addresses on the three envelopes are 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. $\frac{5}{6}$

Answer 1

The correct option is B $\frac{1}{3}$

Favourable ways = $3!(1-\frac{1}{1}!+\frac{1}{2!}-\frac{1}{3!})$
=2
Total ways =3!
$\therefore$ Probability $=\frac{2}{3!}=\frac{1}{3}$