child's play vs fireman

child's play and fireman both are nouns.

Word	Noun	Adjective	Verb	Adverb
child's play	Yes	No	No	No
fireman	Yes	No	No	No

As nouns, fireman is a hyponym of child's play; that is, fireman is a word with a more specific, narrower meaning than child's play:

child's play: activity by children that is guided more by imagination than by fixed rules
fireman: play in which children pretend to put out a fire

Other hyponyms of child's play include house, doctor.

child's play (noun)	fireman (noun)
any undertaking that is easy to do	play in which children pretend to put out a fire
activity by children that is guided more by imagination than by fixed rules	a member of a fire department who tries to extinguish fires
	a laborer who tends fires (as on a coal-fired train or steamship)
	a pitcher who does not start the game