4. In a company of 8 people, each person is acquainted with exactly 6 others. In how many ways can four people be chosen such that any two of them are acquainted? (We assume that if A is acquainted with B, then B is also acquainted with A, and that a person is not acquainted with themselves, as the concept of acquaintance applies to two different people.)
Answer: 16.

Solution. Each person in the company does not know $8-1-6=1$ person in this company. This means the company can be divided into four pairs of strangers. From each pair, we can only take one person to form a company of four people who are all acquainted with each other. The selection of such a company consists of four steps, each with two choices (from each pair), and by the multiplication rule, the company can be chosen in $2^{4}=16$ ways.

Criteria. It is shown that each person is not acquainted with exactly one of the others and only: 1 point.

It is indicated that exactly one person must be chosen from each pair of strangers, but the calculations are incorrect: 3 points.