PASCAL 1997 Problem 19

Three balls numbered 1,2, and 3 are placed in a bag. A ball is drawn from the bag and the number is recorded. The ball is returned to the bag. After this has been done three times, what is the probability that the sum of the three recorded numbers is less than 8?

Answer Choices
A. \frac{23}{27}
B. \frac57
C. \frac59
D. \frac89
E. \frac{22}{27}