Task 2. (Option 1)

At the bus depot, there are 5 red, 6 blue, and 5 yellow buses. A convoy of 7 buses is randomly formed. What is the probability that the first bus in the convoy is red, and among the rest there are no red buses, but exactly 4 blue ones?
Solution: There are a total of $5+6+5=16$ buses. It is necessary for the first bus to be red - the probability is $\frac{5}{16}$. From the remaining 15, 4 blue, 2 yellow, and 0 red buses are chosen, so the probability is $\frac{C_{6}^{4} \cdot C_{5}^{2} \cdot C_{4}^{0}}{C_{15}^{6}}$. The desired probability is obtained by multiplying the two probabilities: $\frac{5 C_{6}^{4} \cdot C_{5}^{2} \cdot C_{4}^{0}}{16 C_{15}^{6}}$. We will calculate these expressions separately: $C_{4}^{0}=1 ; C_{5}^{2}=\frac{5 \cdot 4}{1 \cdot 2}=10 ; C_{6}^{4}=\frac{6 \cdot 5 \cdot 4 \cdot 3}{1 \cdot 2 \cdot 3 \cdot 4}=15 ; C_{15}^{6}=\frac{15 \cdot 14 \cdot 13 \cdot 12 \cdot 11 \cdot 10}{1 \cdot 2 \cdot 3 \cdot 4 \cdot 5 \cdot 6}=505$.

Substitute the obtained results into the answer: $\frac{5 \cdot 15 \cdot 10 \cdot 1}{16 \cdot 505}=\frac{750}{8080}=\frac{75}{808}$.

Answer: $\frac{75}{808}$.