## 20. Stewardesses

To serve a transatlantic flight of an airliner, three stewardesses are required, who are chosen by lot from 20 girls competing for these positions. Seven of them are blondes, the rest are brunettes. What is the probability that among the three selected stewardesses there will be at least one blonde and at least one brunette?
20. If among the three chosen girls there is at least one blonde and one brunette, this means that the cases where all stewardesses turned out to be brunettes

$$
\left(\text { probability of this: } \frac{13 \cdot 12 \cdot 11}{20 \cdot 19 \cdot 18}\right)
$$

or all - blondes

$$
\left(\text { probability of this: } \frac{7 \cdot 6 \cdot 5}{20 \cdot 19 \cdot 18}\right) \text {. }
$$

Therefore, the desired probability is

$$
1-\frac{13 \cdot 12 \cdot 11}{20 \cdot 19 \cdot 18}-\frac{7 \cdot 6 \cdot 5}{20 \cdot 19 \cdot 18}=0.718
$$