7. The commission consists of 11 people. The materials that the commission works on are stored in a safe. How many locks should the safe have, and how many keys should each member of the commission be provided with, so that access to the safe is possible when a majority of the commission members gather, but not possible if fewer than half of the members gather?
7. According to the problem statement, for any five members of the committee, there should be a lock for which the key is absent from all these committee members (but is present with each of the six absent members, since the presence of any of the nine absent members already makes the meeting of the committee possible). Thus, the smallest possible number of locks is equal to the number of ways to choose five members from the 11 members of the committee, i.e., the number of combinations of 11 elements taken 5 at a time:

$$
C_{11}^{5}=\frac{11 \cdot 10 \cdot 9 \cdot 8 \cdot 7}{1 \cdot 2 \cdot 3 \cdot 4 \cdot 5}=462
$$

Since each lock should have six keys, the total number of keys will be

$$
462 \cdot 6=2772
$$

Each member of the committee will have

$$
2772: 11=252
$$

keys.

For the conditions stated in the problem to be met, the keys must be distributed in a specific way. Specifically, the six keys to each of the $C_{11}^{5}$ locks should be held by a specific group of six committee members, and for each group of six members, there should be a lock for which the key is held by this group of six members and only by them. Then, a meeting of the committee will be impossible if six (or more) members of the committee are absent.

If the number of committee members were $n$ and it were required that the safe could be opened with the presence of $m$ members, then the number of locks on the safe should be

$$
C_{n}^{m-1}=\frac{n(n-1) \ldots(n-m-2)}{1 \cdot 2 \cdot 3 \ldots(m-1)}
$$

and the number of keys each committee member should have is

$$
\frac{m}{n} C_{n}^{m-1}=\frac{m(n-1) \ldots(n-m-2)}{1.2 \cdot 3 \ldots(m-1)}
$$

The obtained answer indicates that such a method of storing documents is practically unfeasible (even with a relatively small committee, opening the safe would take an entire day).