Permutation vs Combination
Permutations (nPr) count ordered arrangements. Combinations (nCr) count unordered selections and groupings.
Grade 11th · Mathematics · Algebra
Permutations, Combinations & Binomial Theorem: Core Theory, Derivations & Solved Proofs
In-depth theoretical breakdown, mathematical derivations, foundational axioms, and step-by-step proofs. covering Permutations, Combinations & Binomial Theorem for Class 11th Mathematics.
Science StreamAdvanced Level
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Essential Formulas & Mathematical Definitions
nPr = n! / (n - r)!
nCr = n! / [r!(n - r)!]
nCr + nC(r-1) = (n+1)Cr
(a + b)ⁿ = Σ nCr aⁿ⁻ʳ bʳ
Tr+1 = nCr aⁿ⁻ʳ bʳ
Binomial General Term (Tr+1)
The (r+1)th term in the expansion of (a+b)ⁿ is Tr+1 = nCr aⁿ⁻ʳ bʳ. If n is even, middle term is T(n/2 + 1).
Algebra — Core Theory, Derivations & Solved Proofs
Detailed educational reference for Permutations, Combinations & Binomial Theorem. Designed for Class 11th students preparing for board exams and competitive entrance tests.
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Exam Day Revision & Problem Solving Checklist
- ✓Apply string/block method and gap method in restricted permutations
- ✓Use Pascal's identity nCr + nC(r-1) = (n+1)Cr
- ✓Review Core Theory, Derivations & Solved Proofs before tackling multi-step practice questions
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High-Yield Exam Strategy & Scoring Tips
Step-by-Step Mark Allocation
Always state the governing principle or formula first, write given values with standard SI units, substitute clearly, and highlight the final numerical answer with units in a box for full step marking.
Common Calculation Traps
Watch for unit prefixes (cm to m, minutes to seconds, g to kg, degrees to radians). In coordinate and ray optics problems, double-check Cartesian sign conventions before computing.
Recommended Practice & Calculation Tools
Test your understanding and perform instant calculations with these free online utilities.
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Frequently Asked Exam Questions & Concept Clarifications
How many diagonals exist in an n-sided polygon?
Number of diagonals = nC2 - n = n(n - 3) / 2.