If three letters can be posted to any one of the 5 different addresses, then the probabili…

Question

If three letters can be posted to any one of the 5 different addresses, then the probability that the three letters are posted to exactly two addresses is :

Accepted Answer

We have 3 letters and 5 addresses, where 3 letters are posted to exactly 2 addresses. First, we will select 2 addresses in ${ }^5 C_2$ ways.

Now, 3 letters can be posted to exactly 2 addresses in 6 ways.

$$\begin{aligned}
\therefore \text { Probability }=\frac{{ }^5 C_2 \times 6}{5^3} & \
& =\frac{60}{125}=\frac{12}{25}
\end{aligned}$$

Solutions · 1