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

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:
  1. $\frac{18}{25}$
  2. $\frac{12}{25}$
  3. $\frac{6}{25}$
  4. $\frac{4}{25}$

Solution

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

Asked in: JEE Main 2024 (06 Apr Shift 2)

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