Question

$3$ letters are to be placed in $3$ addressed envelopes. If the letters are placed randomly, then the probablity that all letters are in right envelopes, is

• A. $\frac{1}{4}$
• B. $\frac{1}{6}$
• C. $\frac{1}{3}$
• D. $\frac{1}{8}$

Answer 1

The correct option is B $\frac{1}{6}$

For $3$ letters and $3$ envelopes, the total number of ways of putting a letter in an envelope is $3!=6$
The total number of ways of all letters to be put in right envelope is only one.
Hence, the required probablity is $\frac{1}{3!}=\frac{1}{6}$