Question 20
In a school there are $b$ teachers and $c$ students. Suppose that
(i) each teacher teaches exactly $k$ students; and
(ii) for each pair of distinct students, exactly $h$ teachers teach both of them.
Show that
$$
\frac{b}{h} = \frac{c(c-1)}{k(k-1)}
$$
(i) each teacher teaches exactly $k$ students; and
(ii) for each pair of distinct students, exactly $h$ teachers teach both of them.
Show that
$$
\frac{b}{h} = \frac{c(c-1)}{k(k-1)}
$$