Question

32 члена Совета директоров компании из 4 кандидатов выбирают 33-го члена Совета. При этом каждый член Совета голосует ровно за одного из них. После голосования составляется протокол, в котором указывается только количество голосов за каждого из кандидатов. Сколько различных протоколов голосования может получиться?

Answer 1

Это раздел комбинаторики.
Если каждый из 32-х может проголосовать за одного из 4-х, то:
32*32*32*32 = 1'048'576 протоколов.

Answer 2

Calculation of the Number of Possible Voting Protocols

To determine the number of different voting protocols that can be obtained, we need to consider the number of ways in which the 33rd member of the Board of Directors can be chosen and the number of ways in which the remaining 32 members can vote for the candidates.

1. Choosing the 33rd Member: - Since there are 4 candidates and only one position available, the 33rd member can be chosen in 4 ways.

2. Voting by the 32 Members: - Each of the 32 members can vote for one of the 4 candidates. - Since each member can vote for any of the 4 candidates, there are 4^32 possible combinations of votes.

3. Calculation: - To find the total number of different voting protocols, we multiply the number of ways to choose the 33rd member by the number of possible combinations of votes by the 32 members. - Therefore, the total number of different voting protocols is: 4 * (4^32).

Answer:

The number of different voting protocols that can be obtained is 4 * (4^32).