1. **State the problem:** We have a group of students: 4 Ateneans, 3 Lasallians, 2 Dilimanians, and 1 Thomasian, totaling $4+3+2+1=10$ students. We want to find the probability that when 4 students are randomly chosen, the 3 Atenean siblings are included. 2. **Formula for probability:** $$\text{Probability} = \frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}}$$ 3. **Total number of possible outcomes:** Choosing any 4 students from 10: $$\binom{10}{4} = \frac{10!}{4!\times 6!} = 210$$ 4. **Number of favorable outcomes:** We want the 3 Atenean siblings to be included. So, these 3 are fixed in the chosen group. We need to choose the 4th student from the remaining students (total 10 - 3 = 7 students). Number of ways to choose the 4th student: $$\binom{7}{1} = 7$$ 5. **Calculate the probability:** $$\text{Probability} = \frac{7}{210}$$ 6. **Simplify the fraction:** $$\frac{7}{210} = \frac{\cancel{7}^1}{\cancel{7}30} = \frac{1}{30}$$ **Final answer:** $$\boxed{\frac{1}{30}}$$