AMC 8 1986 Problem 24

The $600$ students at King Middle School are divided into three groups of equal size for lunch. Each group has lunch at a different time. A computer randomly assigns each student to one of three lunch groups. The probability that three friends, Al, Bob, and Carol, will be assigned to the same lunch group is approximately $\text{(A)}\ \frac{1}{27} \text{(B)}\ \frac{1}{9} \text{(C)}\ \frac{1}{8} \text{(D)}\ \frac{1}{6} \text{(E)}\ \frac{1}{3}$