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JEE Main2005MathematicsBinomial TheoremActual

The value of ⁵⁰ C ₄+ _ r =1 ^6 ^ 56-r C ₃ is

Options

  1. A⁵⁵ C ₄
  2. B⁵⁵ C ₃
  3. C⁵⁶ C ₃
  4. D⁵⁶ C ₄

Correct answer

D. ⁵⁶ C ₄

Step-by-step solution

aligned & ⁵⁰ C ₄+ _ r =1 ^6 ^ 56-r C ₃ & ⁵⁰ C ₄+ [ ⁵⁵ C ₃+ ⁵⁴ C ₃+ ⁵³ C ₃+ ⁵² C ₃+ ⁵¹ C ₃+ ⁵⁰ C ₃ ] & = ( ⁵⁰ C ₄+ ⁵⁰ C ₃ )+ ⁵¹ C ₃+ ⁵² C ₃+ ⁵³ C ₃+ ⁵⁴ C ₃+ ⁵⁵ C ₃ & ( ⁵¹ C + ⁵¹ C )+ ⁵² C ₃+ ⁵³ C ₃+ ⁵⁴ C ₃+ ⁵⁵ C ₃ & ⁵⁵ C ₄+ ⁵⁵ C ₃= ⁵⁶ C ₄ . aligned

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