## Task B-3.4.

A restaurant offers its guests a selection of cold meat cuts, fish pâté, and vegetable salad for appetizers. For soup, guests can choose from chicken soup, beef soup, fish soup, broccoli soup, and asparagus soup. For the main course, the restaurant offers a fish, meat, or vegetarian plate, and for dessert, a vegan cake or vegan ice cream. If a guest chooses one dish from each course, what is the probability that they will randomly select a completely vegetarian meal (a meal without meat and fish)?
## Solution.

The set of all elementary outcomes is the set of all possible meal selections, that is, the set of all possible ordered quadruples of the form (appetizer, soup, main course, dessert).

Here, an appetizer can be chosen in 3 ways, a soup in 5 ways, a main course in 3 ways, and a dessert in 2 ways. Therefore, there are a total of $3 \cdot 5 \cdot 3 \cdot 2=90$ outcomes.

For outcomes that correspond to the event, the appetizer can be chosen in 1 way, the soup in 2 ways, the main course in 1 way, and the dessert in 2 ways.

Thus, the event that a vegetarian meal is chosen corresponds to $1 \cdot 2 \cdot 1 \cdot 2=4$ outcomes.

From all of the above, the desired probability is $\frac{4}{90}=\frac{2}{45}$.

1 point