1995 AHSME Problem 20

If a,b and c are three (not necessarily different) numbers chosen randomly and with replacement from the set \{1,2,3,4,5 \}, the probability that ab + c is even is

\mathrm{(A) \ \frac {2}{5} } \qquad \mathrm{(B) \ \frac {59}{125} } \qquad \mathrm{(C) \ \frac {1}{2} } \qquad \mathrm{(D) \ \frac {64}{125} } \qquad \mathrm{(E) \ \frac {3}{5} }

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