English uses an before any word that opens with a vowel sound and a before any word that opens with a consonant sound. Anthropologist starts with the vowel sound an, so the article that belongs in front of it is an, giving An anthropologist by profession, he is also a trained classical singer.
Walk through why the rest fail. A anthropologist breaks the vowel sound rule directly. The anthropologist would only work if the sentence were referring back to a specific, already identified anthropologist, but here the sentence is simply introducing someone's profession for the first time, so the indefinite article is needed instead. As anthropologist leaves the phrase incomplete, because as used this way needs its own article before the noun, as in as an anthropologist.
The only sentence that respects both the article rule and basic sentence structure is An anthropologist by profession, he is also a trained classical singer, confirming option 4 as correct.
Ravi had _________ younger brother who taught at _________ university. He was widely regarded as _________ honorable man.
Select the option with the correct sequence of articles to fill in the blanks.