# Laboratory Work 7 — Combinatorics and Descriptive Statistics

> Seventh laboratory work of **Computer Discrete Mathematics**. You implement the
> counting formulas of **combinatorics** — permutations, arrangements, and
> combinations — compute the basic **descriptive statistics** of a dataset (mean,
> variance, standard deviation), and generate combinatorial objects explicitly.

## At a glance

| | |
|---|---|
| **Topic** | Combinatorics (permutations, arrangements, combinations) and descriptive statistics (mean, variance, standard deviation) |
| **Prerequisite lectures** | [L13 — Probabilities](../../Lectures/CDM-L13.md) |
| **Deliverable** | Source code + report (see [5report.md](5report.md)) |
| **Grading** | Banded: Easy 60–74 / Medium 75–89 / Hard 90–100 (see [4task.md](4task.md)) |

## Contents

| # | Part | File |
|:--:|---|---|
| 1 | Objective | [1purpose.md](1purpose.md) |
| 2 | Methodical guidelines (theory & algorithms) | [2method.md](2method.md) |
| 4 | Task and order of execution | [4task.md](4task.md) |
| 5 | Report contents | [5report.md](5report.md) |
| 6 | Control questions | [6questions.md](6questions.md) |

## Conventions

- **Language** — source code and the report are in **English**.
- **Implement it yourself — no built-in shortcuts.** Do not call a library or
  built-in that performs the core task for you (e.g. no `HashSet`/`set()`/`Set`
  for sets, no library graph/relation type, no `math.gcd`, no `eval`). Build the
  mechanism from basic primitives — arrays/lists, loops, arithmetic, strings.
- **Deliverable** — submit the source code **and** a report structured as in
  [5report.md](5report.md); the code must reproduce the example outputs in
  [4task.md](4task.md).
- **Self-contained theory** — everything needed is in [2method.md](2method.md);
  no external material is required.

## Summary

**Combinatorics** counts the ways to arrange and select objects: the number of
orderings of a set (**permutations**), of ordered selections of $k$ from $n$
(**arrangements**), and of unordered selections (**combinations**). These counts
underpin probability, which is why the work pairs them with the basic
**descriptive statistics** of a dataset — its **mean** (mathematical
expectation), **variance**, and **standard deviation**. A final task moves from
*counting* the objects to *generating* them. The tasks are grouped into three
difficulty bands.