What is the explaination of the grammaticality judgments for the following NPs$,$ in terms of C$-$selection restrictions, where the NP in $"$My hope with the field of linguistics" is ungrammatical

a$)$ The noun hope C$-$selects an embedded sentence headed by that, but not a PP headed by with. b$)$ The noun hope C$-$selects a PP headed by that, but not an embedded sentence headed by that. c$)$ The noun hope can C$-$select any kind of syntactic complement.

d$)$ Both statements $($a$)$ and $($b$)$ are correct.

e$)$ Both statements $($b$)$ and $($c$)$ are correct.