Answer:
In the sentence 3. Maria loves to go dancing, "to go dancing" is not a noun phrase.
Step-by-step explanation:
A noun phrase should present a noun and other words that modify such noun (determiners or modifiers). It functions as a noun would function in the structure of the sentence. The phrase "to go dancing" does not fit such description. Thus, it is not a noun phrase.
As a matter of fact, the phrase "to go dancing" is an infinitive phrase. Infinitive phrases are comprised of a verb in the infinitive form (to + base form of the verb) and modifiers or other words related to the infinitive. Infinitive phrases can function as nouns, adjectives, or adverbs in a sentence. In the specific sentence we are studying here, "to go dancing" functions as a noun, being the object of the verb "loves".
3. Maria loves to go dancing.
Maria - subject
loves - verb
to go dancing - object