Twenty four people are part of three committees which are to look at research, teaching, and administration respectively. No two committees have any member in common. No two committees are of the same size. Each committee has three types of people: bureaucrats, educationalists, and politicians, with at least one from each of the three types in each committee. The following facts are also known about the committees:
- The numbers of bureaucrats in the research and teaching committees are equal, while the number of bureaucrats in the research committee is $75\%$ of the number of bureaucrats in the administration committee.
- The number of educationalists in the teaching committee is less than the number of educationalists in the research committee. The number of educationalists in the research committee is the average of the numbers of educationalists in the other two committees.
- $60\%$ of the politicians are in the administration committee, and $20\%$ are in the teaching committee.
What is the number of bureaucrats in the administration committee?