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AP EAMCET202124 Aug 2021Evening ShiftMathematicsBinomial TheoremActual

The value of _ r=0 ^4 ^ (19-r) C₃+ ¹⁵ C₄ is equal to

Options

  1. A²¹ C₄
  2. B¹⁹ C ₄
  3. C²⁰ C₄
  4. D¹⁶ C ₄

Correct answer

C. ²⁰ C₄

Step-by-step solution

_ r=0 ^4 ^ 19-r C₃+ ¹⁵ C₄= ¹⁹ C₃+ ¹⁸ C₃+ ¹⁷ C₃+ ¹⁶ C₃+ ¹⁵ C₃+ ¹⁵ C₄ aligned & = ¹⁹ C₃+ ¹⁸ C₃+ ¹⁷ C₃+ ¹⁷ C₄ & = ¹⁹ C₃+ ¹⁸ C₃+ ¹⁸ C₄ & = ¹⁹ C₃+ ¹⁹ C₄ & = ²⁰ C₄ aligned

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