1988 AHSME Problem 28

An unfair coin has probability p of coming up heads on a single toss. Let w be the probability that, in 5 independent toss of this coin, heads come up exactly 3 times. If w = 144 / 625, then

\begin{array}{l} \textbf{(A)}\ p\text{ must be }\tfrac{2}{5}\qquad \textbf{(B)}\ p\text{ must be }\tfrac{3}{5}\qquad\\ \textbf{(C)}\ p\text{ must be greater than }\tfrac{3}{5}\qquad \textbf{(D)}\ p\text{ is not uniquely determined}\qquad\\ \textbf{(E)}\ \text{there is no value of } p \text{ for which }w =\tfrac{144}{625} \end{array}

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