(2) C (below 7 and above 3) = 35

It can be understood as follows:

(1) Eight blackboards are arranged in a row, randomly inserted into three partitions, and divided into four parts, corresponding to the blackboards distributed by four schools. Because some schools are allowed to have no blackboards, that is to say, eight blackboards can freely arrange three partitions, that is, C (lower 1 1, upper 8).

(2) Eight blackboards are arranged in a row with seven gaps and randomly inserted into three partitions, namely C (7 blackboards below and 3 blackboards above).