price of admission vs admission

price of admission and admission both are nouns.

Word	Noun	Adjective	Verb	Adverb
price of admission	Yes	No	No	No
admission	Yes	No	No	No

As nouns, price of admission and admission are synonyms defined as:

Other synonyms of price of admission include admission charge, admission fee, admission price, entrance fee, entrance money.

price of admission (noun)	admission (noun)
the fee charged for admission	the act of admitting someone to enter
	the right to enter
	an acknowledgment of the truth of something
	the fee charged for admission