PROBS

If there are 2 professors: $\dfrac{8\times7}2\times6\times13=2184$

If there are 2 associate professors: $8\times\dfrac{6\times5}2\times13=1560$

If there are 2 assistant professors: $8\times6\times\dfrac{13\times12}2=3744$

So, $2184+1560+3744=7488$

1 professor can be chosen in 8 ways,1 associate professor can be chosen in 6 ways and 1 assistant professor can be chosen in 13 ways.In all,3 professors can be chosen if each must be included in 8 * 6 * 13 =624 ways.The remaining professor can be chosen from the remaining 24 professors in 24 ways. Total ways of selecting 4 professors is 624 * 24 = 14976 ways. But these processes can be performed back and forth so the answer is divided by 2.So the final answer is 14976÷2=7488