📚 Key Concepts
Fundamental Principle of CountingFactorial notation (n!)Permutations (arrangements)Combinations (selections)Circular permutationsRepetition allowed/not allowedPermutation with restrictionsPascal's triangle
🎯 Key Formulas
Factorial: n! = n × (n-1)!Permutations:- nPr = n!/(n-r)!
- With repetition = n^r
- Circular = (n-1)!
Combinations:- nCr = n!/[r!(n-r)!]
- nCr = nC(n-r)
Important Results:- nC0 + nC1 + ... + nCn = 2^n
- nC0 = nCn = 1
- nCr + nC(r-1) = n+1Cr
⚠️ Common Mistakes to Avoid
Confusing nPr with nCrWrong factorial calculationsNot considering repetitions properlyIncorrect application of circular permutationForgetting order matters in permutationWrong application of selection rules
📖 Knowledge Prerequisites
Basic counting principlesFactorialsBasic algebraSet theory basics
💡 Tips for Students
Identify if order matters (P) or doesn't (C)Draw tree diagrams for complex problemsCheck if repetition is allowedUse smaller numbers to verify logicRemember nCr = nC(n-r)
👉 Practice Recommedations
Start with simple counting problemsPractice factorial calculationsSolve word problemsWork on selection problemsApply in real-life scenariosPractice problems with restrictionsCombine P and C concepts
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