1. Total number of ways to post 3 letters

Each of the 3 letters can be sent to any one of the 5 addresses.

So, total number of possible postings is $5^3=125.$

2. Favourable cases: exactly two addresses are used

We need the 3 letters to be posted to exactly 2 distinct addresses.

This can be counted in two steps:

Step 1: Choose the 2 addresses

Out of 5 addresses, choose 2: $\binom{5}{2}=10.$

Step 2: Distribute 3 letters among these 2 chosen addresses so that both addresses are used

For 3 distinct letters and 2 chosen addresses:

• Total ways to assign them to the 2 addresses: $2^3=8.$
• But subtract the 2 cases where all 3 letters go to only one address.

So favourable distributions for the chosen pair are: $2^3-2=8-2=6.$

Thus total favourable cases are: $\binom{5}{2}\times 6=10\times 6=60.$

3. Required probability

$P=\frac{60}{125}=\frac{12}{25}.$

4. Compare with options

$\frac{12}{25}$ corresponds to Option B.

5. Comparison with stored answer

Stored correct answer is B, which matches our result.