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COMEDK2023MathematicsBinomial Theorem

Find ^n C₂₁ , if ^n C₁₀= ^n C₁₂

Options

  1. A1
  2. B21
  3. C22
  4. D2

Correct answer

C. 22

Step-by-step solution

We know that if ^n C_x= ^n C_y , then either x=y or x+y=n Since, ^n C₁₀= ^n C₁₂ aligned 10+12 & =n n & =22 Now, ^n C₂₁ & = 22 21 & = 22 ! (22-21) ! 21 ! = 22 ! 1 ! 21 ! = 22 21 ! 1 21 ! =22 aligned

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