NDA2019MathematicsPermutation and CombinationActual
What is C (47,4)+ C (51,3)+ C (50,3)+ C (49,3)+ C (48,3)+ C (47,3) equal to?
Options
- AC (47,4)
- BC (52,5)
- CC (52,4)
- DC (47,5)
Correct answer
C. C (52,4)
Step-by-step solution
aligned & ⁴⁷ C₄+ ⁴⁷ C₃+ ⁴⁸ C₃+ ⁴⁹ C₃+ ⁵⁰ C₃+ ⁵¹ C₃ & ^n C_r+ ^n C_ r-1 = ^ n+1 C_r & we get & ⁴⁸ C₄+ ⁴⁸ C₃+ ⁴⁹ C₃+ ⁵⁰ C₃+ ⁵¹ C₃ & = ⁴⁹ C₄+ ⁴⁹ C₃+ ⁵⁰ C₃+ ⁵¹ C₃ & = ⁵⁰ C₄+ ⁵⁰ C₃+ ⁵¹ C₃ aligned aligned & = ⁵¹ C₄+ ⁵¹ C₃ & = ⁵² C₄ aligned