Of all the students in a certain dormitory, $$\frac1 2$$ are first-year students and the rest are second-year students. If $$\frac4 5$$ of the first-year students have not declared a major and if the fraction of second-year students who have declared a major is 3 times the fraction of first-year students who have declared a major, what fraction of all the students in the dormitory are second-year students who have not declared a major?
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A$$\frac{1}{15}$$
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B$$\frac{1}{5}$$
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C$$\frac{4}{15}$$
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D$$\frac{1}{3}$$
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E$$\frac{2}{5}$$