KCET2024MathematicsPermutation and Combination
The value of ⁴⁹ C₃+ ⁴⁸ C₃+ ⁴⁷ C₃+ ⁴⁶ C₃+ ⁴⁵ C₃+ ⁴⁵ C₄ is
Options
- A⁵⁰ C₄
- B⁵⁰ C₃
- C⁵⁰ C₂
- D⁵⁰ C₁
Correct answer
A. ⁵⁰ C₄
Step-by-step solution
^n C_r+ ^n C_ r+1 = n+1 r+1 Given, ⁴⁹ C₃+ ⁴⁸ C₃+ ⁴⁷ C₃+ ⁴⁶ C₃+ ⁴⁵ C₃+ ⁴⁵ C₄= ⁴⁹ C₃+ ⁴⁸ C₃+ ⁴⁷ C₃+ ⁴⁶ C₃+ ⁴⁶ C₄= ⁴⁹ C₃+ ⁴⁸ C₃+ ⁴⁷ C₃+ ⁴⁷ C₄= ⁴⁹ C₃+ ⁴⁸ C₃+ ⁴⁸ C₄= ⁴⁹ C₃+ ⁴⁹ C₄= ⁵⁰ C₄