If three letters can be posted to any one of the 5 different... | Mathematics | SolveeIt | Solveeit

Today, August 18

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:

A

$\frac{12}{25}$

B

$\frac{18}{25}$

C

$\frac{4}{25}$

D

$\frac{6}{25}$

Answer

$\frac{12}{25}$

Explanation

Solution

$\text{Total methods} = 5^3$

$\text{Favorable} = ^3C_2 \times (2^3 - 2) = 60$

$\text{Probability} = \frac{60}{125} = \frac{12}{25}$