Question

Three letters, to each of which corresponds an addressed envelope are placed in the envelopes at random. The probability that all letters are placed in the right envelopes is:

• A. $\frac{1}{3}$
• B. $1$
• C. $\frac{1}{6}$
• D. $0$

Answer 1

Answer: (C)

$\frac{1}{6}$

Three letters can be placed in their right envelopes in 1 way only.
$n\left(E\right)=1$
Three letters can be placed in any of the 3 envelopes in ${}^3{p}_3=3\times 2=6$ ways.
$n\left(S\right)=3\times 2\times 1=6$
$P\left(E\right)=\frac{n\left(E\right)}{n\left(S\right)}=\frac{1}{6}$