To solve this problem, we need to understand the specific role of RNA polymerase III in eukaryotic transcription.$\newline$Let's analyze the options:$\newline \bullet$Option 1: Transcribes rRNAs (28S, 18S, and 5.8S)$\newline$ - This is incorrect because RNA polymerase I is responsible for transcribing the larger rRNA components (28S, 18S, and 5.8S).$\newline \bullet$Option 2: Transcribes tRNA, 5S rRNA, and snRNA$\newline$ - This is correct. RNA polymerase III is responsible for transcribing tRNA, 5S rRNA, and some small nuclear RNAs (snRNA).$\newline \bullet$Option 3: Transcribes precursor of mRNA$\newline$ - This is incorrect because RNA polymerase II transcribes the precursor of mRNA (pre-mRNA).$\newline \bullet$Option 4: Transcribes only snRNAs$\newline$ - This is incorrect because RNA polymerase III transcribes more than just snRNAs; it also transcribes tRNA and 5S rRNA.$\newline$Therefore, the correct option is Option 2: Transcribes tRNA, 5S rRNA, and snRNA.