The first sentence has الطالبُ as its subject. Hence that word is in the nominative and has no nunation since it is definite. The predicate of the sentence is في البيتِ which is a prepositional phrase. The noun البيتِ follows the preposition في so it must, must, must, be in the genitive case. Since البيتِ is definite it cannot and must not have nunation, so it takes only one kasra.

The second sentence أنت as its subject. That word is a pronoun, so it will not take a case ending. المديرُ is a predicate and so must be in the nominative case. In fact, أنتَ المديرُ is itself an equational sentence. However following أنتَ المديرُ in the sentence above is a prepositional phrase في هذا المكتبِ You should know that هذا المكتبِ is one unit (this was discussed in Chapter One). هذا is not a word that takes case but المكتبِ is a regular noun and it will always have a case. Since هذا المكتبِ is one unit, المكتبِ is put into the genitive because of the preposition في

The third sentence is very similar to the second. The first two words المكتبةُ قريبةٌ can themselves form an equational sentence. The first word is the subject, the second is the predicate. مِن الجامعةِ is prepositional phrase so الجامعةِ must be genitive. Since الجامعةِ is definite it gets only one kasra. I hope that you did not confuse the preposition مِنْ with the interrogative مَنْ

Before you do any drills at the end of this chapter, read the next section on The Idaafa.