Explanation
Correct answer: A.
Choice A is the best answer. The convention being tested is the punctuation of supplementary elements within a sentence. This choice correctly uses a comma to separate the supplementary adverb "however" from the preceding main clause ("only...competitions"), and it uses a colon to introduce the list of dances that follows ("rumba…jive"). Further, placing the colon after "however" rather than before indicates that the information in the preceding main clause (only...competitions) is contrary to what might be assumed from the information in the previous sentence (Latin America has many more dance forms).
Why the other choices are wrong
Choice B
Choice B is incorrect. The comma after "however" can’t be used in this way to introduce a series ("rumba...jive").
Choice C
Choice C is incorrect because it isn’t conventional to use a semicolon in this way to introduce a series of items, such as the list of dances.
Choice D
Choice D is incorrect because placing the semicolon after "competitions" illogically indicates that the following list of five Latin American dances ("rumba...jive") is contrary to the information in the previous clause (only five Latin American dances are included in international ballroom dance competitions).