# 1. Objective / Мета роботи

**Implement the counting formulas of combinatorics and the basic descriptive
statistics of a dataset, and generate combinatorial objects.**

By the end of the work the student should be able to:

- compute the number of **permutations** $P_n = n!$, **arrangements**
  $A_n^k = \dfrac{n!}{(n-k)!}$, and **combinations**
  $C_n^k = \dfrac{n!}{k!\,(n-k)!}$, and explain when **order matters**;
- compute the **mean** (mathematical expectation), **variance**, and **standard
  deviation** of a set of values;
- **generate and list** the actual permutations, arrangements, or combinations of
  a given set, not merely count them;
- compute factorials and the counts **efficiently**, avoiding needless overflow;
- reason about the **time complexity** of counting versus generating.

The work provides the combinatorial groundwork for probability and prepares the
tools used to reason quantitatively about finite sample spaces.