JEE MAIN - Mathematics (2024 - 6th April Evening Shift - No. 7)
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 :
$$\frac{18}{25}$$
$$\frac{12}{25}$$
$$\frac{6}{25}$$
$$\frac{4}{25}$$
Explanation
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.
$$\begin{aligned} \therefore \text { Probability }=\frac{{ }^5 C_2 \times 6}{5^3} & \\ & =\frac{60}{125}=\frac{12}{25} \end{aligned}$$
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