In a class of 30 students, 12 are boys and 18 are girls. The teacher randomly selects one student to be the class representative and another student to be the assistant. What is the probability that both positions will be filled by girls?
The probability is 153/435.

Here's the reasoning:
1. There are 30 students in total, with 18 being girls.
2. When selecting the first position (class representative), there is an 18/30 chance it will be a girl (since there are 18 girls out of 30 students).
3. After choosing one girl for the first position, there are now 17 girls left among the remaining 29 students.
4. So when selecting the second position (assistant), there is a 17/29 chance it will also be a girl.
5. To find the probability that both positions are filled by girls, multiply the probabilities for each selection: (18/30) x (17/29) = 306/870.
6. Simplify the fraction: 306/870 = 153/435.