Question 6
There are $n\ge2$ classes organizing $m\ge1$ extracurricular clubs. Every class has students participating in at least one club. Each club has participants from exactly $a$ classes. For any two clubs, at most $b$ classes have participants in both.
a) Find $m$ when $n=8,a=4,b=1$.
b) Prove $n\ge20$ when $m=6,a=10,b=4$.
c) Find the smallest $n$ when $m=20,a=4,b=1$.
a) Find $m$ when $n=8,a=4,b=1$.
b) Prove $n\ge20$ when $m=6,a=10,b=4$.
c) Find the smallest $n$ when $m=20,a=4,b=1$.