If three letters can be posted to any one of the 5 different...

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:

Options

A $\frac{18}{25}$
B $\frac{12}{25}$
C $\frac{6}{25}$
D $\frac{4}{25}$

Correct answer

B. $\frac{12}{25}$

Step-by-step solution

\begin{aligned} & \text{ Total method }=5^3 \\ & \text{ faverable }={ }^5 \mathrm{C}_2\left(2^3-2\right)=60 \\ & \text{ probability }=\frac{60}{125}=\frac{12}{25}\end{aligned}

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