Problem $2($based on book $10\mathrm{.}17)$

$[20$pts$]$ In Kerberos:

a$.$ Why can Alice not remain anonymous when requesting a TGT from the KDC$?$

b$.$ Why can Alice remain anonymous in the sense of not needing to use her private key when requesting a ticket to Bob $($what does she use instead and why is this sufficient$)?$

c$.$ Why can Alice remain anonymous $($not needing her private key$)$ when she sends the "ticket to $Bo{b}^{}$ to Bob?