Question 15
In a school there are $2008$ students. Students are members of certain committees. A committee has at most $1004$ members and every two students join a common committee.
a. Determine the smallest possible number of committees in the school.
b. If it is further required that the union of any two committees consists of at most $1800$ students, will your answer in (a) still hold?
a. Determine the smallest possible number of committees in the school.
b. If it is further required that the union of any two committees consists of at most $1800$ students, will your answer in (a) still hold?