Factorials & Permutations
n! factorial, arranging objects in order, permutations with and without repetition. Counting ordered arrangements.
Lessons
1. Intro
(The Goal)
2. When Order Matters
(Arrangements vs selections)
3. Counting Small Cases
(Building intuition)
4. Vocabulary - Factorial
(n! means n × (n-1) × ... × 1)
5. Why Factorial Counts Arrangements
(Multiplying choices)
6. Factorial Examples
(Computing by hand)
7. Permutations of n Distinct Objects
(The basic formula)
8. Partial Permutations
(Choosing r from n)
9. Vocabulary - P(n,r)
(Permutations formula)
10. P(n,r) Examples
(Computing permutations)
11. Permutations with Repetition
(Replacing items)
12. Permutations with Repetition Formula
(n^r arrangements)
13. Repetition Examples
(Passwords and codes)
14. Permutations of Multisets
(Identical items)
15. Multiset Permutation Formula
(Dividing by repetitions)
16. Multiset Examples
(Anagrams with repeats)
17. Circular Permutations
(Arranging in a circle)
18. Circular Permutation Formula
((n-1)! arrangements)
19. Circular Examples
(Round tables and necklaces)
20. Counting Anagrams
(Rearranging letters)
21. Anagram Examples
(Words with repeats)
22. Derangements
(No element in original find)
23. Derangement Formula
(D(n) recursive formula)
24. Derangement Approximation
(D(n) ≈ n!/e)
25. Quiz: Factorials and Basic Permutations
(Knowledge check)
26. Problem - Permutations
(LeetCode 46)
27. Permutations Approach
(Backtracking strategy)
28. Permutations Pseudocode
(Recursive backtracking)
29. Permutations - Implementation
(Python solution)
30. Problem - Permutation Sequence
(LeetCode 60)
31. Permutation Sequence Approach
(Factorial number system)
32. Permutation Sequence Pseudocode
(Greedy construction)
33. Permutation Sequence - Implementation
(Direct computation)
34. Quiz: Multisets and Circular
(Knowledge check)
35. Problem - Permutations II
(LeetCode 47)
36. Permutations II Approach
(Skipping duplicates)
37. Permutations II Pseudocode
(Backtracking with pruning)
38. Permutations II - Implementation
(Duplicate pruning)
39. Pattern - Backtracking for Permutations
(General template)
40. Practice - Next Permutation
(LeetCode 31)
41. Practice - Letter Case Permutation
(LeetCode 784)
42. Practice - Beautiful Arrangement
(LeetCode 526)
43. Application - Password Strength
(Counting possibilities)
44. Application - DNA Sequences
(Biological permutations)
45. Section 10 Recap
(What you learned)