first part can be done in 30p8 ways.
if roberta is in top 3 then we have 29c7 ways to select seven winners.
among 7 we can distribute 7 trophies in 7c7*7! ways
and remaining 1 trophy in 1 ways. trophy should be either 1st 2nd or 3rd prize
since roberta can get only trophies of prize 1 ,2 ,3
this can be done in total 3*7c7*7!*29c7ways