Question

The value of ⁴⁷C₄ + $\sum_{r = 1}^{5}{(52 - r)C_{3}}$

• A. $53C_{3}$
• B. $52C_{4}$
• C. $52C_{5}$
• D. None of these

Answer 1

Answer: (B)

$52C_{4}$

Answer 2

⁴⁷C₄ + $\sum_{r = 1}^{5}{(52 - r)C_{3}}$

$\Rightarrow \underset{}{\overset{\text{47}C_{4}\text{ +}\text{ }^{\text{51}}C_{3}\text{ +}\text{ }^{\text{50}}C_{3}\text{ +}\text{ }^{\text{49}}C_{3}\text{ +}\text{ }^{\text{48}}C_{3}\text{ +}\text{ }^{\text{47}}C_{3}}{︸}}$

⁴⁸C₄

$\Rightarrow \underset{}{\overset{\text{48}C_{4}\text{ +}\text{ }^{\text{51}}C_{3}\text{ +}\text{ }^{\text{50}}C_{3}\text{ +}\text{ }^{\text{49}}C_{3}\text{ +}\text{ }^{\text{48}}C_{3}}{︸}}$

⁴⁹C₄

Similarly proceeding we get ⁵²C₄.