# 4. Task and order of execution / Завдання та порядок виконання

> **Source of tasks.** The three tasks below are taken **exactly** from the
> assignment. Implement the described behaviour; the input/output examples are
> authoritative.

## Order of execution

The tasks are grouped into three difficulty bands. Implement them in order and
test each against its example; your score corresponds to the band of tasks you
complete correctly.

## Easy tasks (60–74 points)

### Task 1 — Combinatorics Calculator
**Objective:** Write a program that calculates the number of **Permutations**,
**Arrangements**, and **Combinations** for given `n` (total elements) and `k`
(selection size).
- **Input:** Total elements (n): `5`; Selection size (k): `3`
- **Output:**
  - Permutations ($P_n$): `120`
  - Arrangements ($A_n^k$): `60`
  - Combinations ($C_n^k$): `10`

## Medium tasks (75–89 points)

### Task 2 — Statistics Analyzer
**Objective:** Implement a program that reads a set of values and calculates the
Mathematical Expectation (Mean), Variance, and Standard Deviation.
- **Input:** Dataset: `{2, 4, 4, 4, 5, 5, 7, 9}`
- **Output:**
  - Mathematical Expectation (E[X]): `5.0`
  - Variance (D[X]): `4.0`
  - Standard Deviation ($\sigma$): `2.0`

## Hard tasks (90–100 points)

### Task 3 — Combinatorial Generator
**Objective:** Write a program that generates and outputs all specific
Permutations, Arrangements, or Combinations for a given set of elements.
- **Input:** Set: `{A, B, C}`; Operation: Generate Permutations
- **Output:**
  - Result: `(A, B, C), (A, C, B), (B, A, C), (B, C, A), (C, A, B), (C, B, A)`
  - Total count: `6`