Yes, VARIETY is a Scrabble word!

Letter values in Scrabble US: V 4, A 1, R 1, I 1, E 1, T 1, Y 4.

Is it a valid word?

VARIETY is a valid word in the official Scrabble dictionary (US), the UK Scrabble Dictionary and Words with Friends (ENABLE).

a collection containing a variety of sorts of things
noticeable heterogeneity
(biology) a taxonomic category consisting of members of a species that differ from others of the same species in minor but heritable characteristics
a show consisting of a series of short unrelated performances
a category of things distinguished by some common characteristic or quality
a difference that is usually pleasant

Also: mixed bag, multifariousness, variety show.