Probability
Letters Posted to Exactly Two Addresses
nta_pyq_2024_apr
Grade 12
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:
$\dfrac{18}{25}$
$\dfrac{12}{25}$
$\dfrac{6}{25}$
$\dfrac{4}{25}$
Step-by-Step Solution
Key Concept: Total ways $=5^3=125$. Favourable: choose 2 addresses from 5 ($^5C_2=10$), then distribute 3 letters into exactly those 2 addresses ($2^3-2=6$). Favourable $=10\times6=60$.
$^5C_2\times(2^3-2)/5^3=60/125=12/25$.
Correct Answer: 2