Core concepts
- 01Permutation: arrangement (order matters).
- 02Combination: selection (order does not matter).
- 03Factorial: n! = n(n−1)(n−2)...1; 0! = 1.
- 04Circular permutation of n distinct objects = (n−1)!
- 05Restrictions handled by treating grouped items as one unit or fixing positions.
Flowchart summary
Selection problems | Order matters? -- Yes --> nPr | No | v nCr
Exam-critical pointers
- ⭐When repetition allowed: arrangements of r items from n = nʳ.
- ⭐Identical items in arrangement: divide by factorial of identicals (n!/p!q!).
- ⭐Selection of at least 1: 2ⁿ − 1.
- ⭐Distinguish 'word formation' MCQs — vowels together / never together patterns.
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