Question

$3$ letters are placed in $3$ envelopes randomly. The probability that only one letter goes in right envelope is

• A. $\frac{1}{2}$
• B. $\frac{1}{3}$
• C. $\frac{1}{6}$
• D. $\frac{2}{3}$

Answer 1

Answer: (A)

$\frac{1}{2}$

Ways the letter can be put into envelopes $=3!=6$
Probability that all are delivered to the correct address $=\frac{1}{6}$
No. of ways one letter is delivered to the correct address $=3ways$
Probability One is delivered to the correct address $=\frac{3}{6}=\frac{1}{2}$

Hence, this is the answer.