Problem 5. Three balls are drawn at once from the urn (condition of problem 4). Find the probability that all the drawn balls will be blue (event $B$).
Solution. The number of possible outcomes $n=C_{10}^{3}$, and the number of outcomes favorable to event $B_{1}, m=C_{5}^{3}$, since three balls are drawn from five blue ones, therefore $p(B)=\frac{C_{5}^{3}}{C_{10}^{3}}=\frac{\frac{5 \cdot 4 \cdot 3}{1 \cdot 2 \cdot 3}}{\frac{10 \cdot 9 \cdot 8}{1 \cdot 2 \cdot 3}}=\frac{1}{12}\left(C_{n}^{k}\right.$ is calculated using the formula for the number of combinations from $\$ 1$ ).

Answer. $p(B)=\frac{1}{12}$.