## Task A-4.1.

In a room, there are seven people. Four of them know exactly one person, and the remaining three people know exactly two people. All acquaintances are mutual.

What is the probability that two randomly selected people do not know each other?
## First solution.

The total number of ordered pairs of people $(A, B)$ is $7 \cdot 6=42$.

The number of ordered pairs $(A, B)$ of people who know each other is $4 \cdot 1+3 \cdot 2=10$.

The probability that two randomly chosen people know each other is $\frac{10}{42}=\frac{5}{21}$.

The desired probability is $1-\frac{5}{21}=\frac{16}{21}$.