2015 AMC 12B Problem 17

An unfair coin lands on heads with a probability of \tfrac{1}{4}. When tossed n times, the probability of exactly two heads is the same as the probability of exactly three heads. What is the value of n ?

\textbf{(A)}\; 5 \qquad\textbf{(B)}\; 8 \qquad\textbf{(C)}\; 10 \qquad\textbf{(D)}\; 11 \qquad\textbf{(E)}\; 13

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.