Kombinacje

The final page covers the concept of combinations. It explains how to calculate the number of ways to choose k elements from an n-element set. The formula for combinations is presented as C(n,k) = n! / (k!(n-k)!).

Definition: A kombinacja is a selection of items from a larger set where the order does not matter.

Two examples are provided to illustrate the application of the combination formula:

1. Calculating the number of ways to choose 2 people from a class of 30.
2. Determining the number of ways to select 3 players from a team of 12.

These examples help students understand how to apply the combination formula in practical scenarios.

Reguła Mnożenia i Dodawania

This page introduces two fundamental principles of combinatorics: the multiplication rule and the addition rule. The reguła mnożenia is explained using practical examples, such as selecting a delegation from a group of boys and girls, and creating meal combinations in a restaurant. The reguła dodawania is briefly introduced, explaining how to count elements from different sets.

Example: A restaurant offers 5 soups, 10 main courses, and 6 desserts. The total number of possible meal combinations is calculated as 5 × 10 × 6 = 300.

Definition: The reguła dodawania states that when choosing an element from two disjoint sets, the total number of choices is the sum of the elements in both sets.