Answer : 3. "3"
Explanation :

to enter will replace entering because – The to-Infinitive (Main Verb) : functions as a Noun, as Adjective, or an Adverb. In this sentence, permitted to enter, to enter is the direct object, the Noun that receives the action of the Verb (Permitted). To enter refers to a thing being done, or, desired to be done Hence, to enter the park is the right usage.