NDA2016MathematicsPermutation and CombinationActual
What is ⁴⁷ C ₄+ ⁵¹ C ₃+ _ j =2 ^5 ^ 52- j C ₃ equal to?
Options
- A⁵² C ₄
- B⁵¹ C ₅
- C⁵³ C ₄
- D⁵² C ₅
Correct answer
A. ⁵² C ₄
Step-by-step solution
aligned & ⁴⁷ C₄+ ⁵¹ C₃+ ⁵⁰ C₃+ ⁴⁹ C₃+ ⁴⁸ C₃+ ⁴⁷ C₃ & = ⁴⁷ C₃+ ⁴⁷ C₄+ ⁴⁸ C₃+ ⁴⁹ C₃+ ⁵⁰ C₃+ ⁵¹ C₃ & ⁴⁸ C₄+ ⁴⁸ C₃+ ⁴⁹ C₃+ ⁵⁰ C₃+ ⁵¹ C₃ & ( ^n C_r+ ^n C_ r+1 = n+1 r+1 ) & = ⁴⁹ C₄+ ⁴⁹ C₃+ ⁵⁰ C₃+ ⁵¹ C₃ & = ⁵⁰ C₄+ ⁵⁰ C₃+ ⁵¹ C₃ & = ⁵¹ C₄+ ⁵¹ C₃ & = ⁵² C₄ aligned