(a) This is the same as putting 30 unlabeled balls into 8 labeled bins where a bin is allowed to receive 0 balls. There is info here

http://www.johndcook.com/TwelvefoldWay.pdf (pdf)

and here

Stars and bars (probability) - Wikipedia, the free encyclopedia

(b) Take answer from (a) and subtract number of ways to place 30 unlabeled balls into 7 labeled bins.