1998 Gauss 8 Problem 15

Michael picks three *different* digits from the set \{1, 2, 3, 4, 5\} and forms a mixed number by placing the digits in the spaces of \square\frac{\square}{\square}. The fractional part of the mixed number must be less than 1. (For example, 4\frac{2}{3}). What is the difference between the largest and smallest possible mixed number that can be formed?

\textbf{(A)}\ 4\frac{3}{5}\quad \textbf{(B)}\ 4\frac{9}{20}\quad \textbf{(C)}\ 4\frac{3}{10}\quad \textbf{(D)}\ 4\frac{4}{15}\quad \textbf{(E)}\ 4\frac{7}{20}

If there are no answer choices shown, enter a numerical answer.

Full credit to this problem is given to the CEMC, you may view all Gauss contests here.