Question

The number of ways in which an examiner can assign 20 marks to 5 questions giving not less than 2 marks to any is (Marks in fraction cannot be given)

• A. $14C_{4}$
• B. $14C_{9}$
• C. $14C_{11}$
• D. None of these

Answer 1

Answer: (A)

$14C_{4}$

Answer 2

Required ways = Coefficient of x²⁰ in (x² + x³ + x⁴ ...)⁵

= Coefficient of x²⁰ in x¹⁰ (1+x+x² + ...)⁵

= Coefficient of x¹⁰ in (1 – x)^-5

= $10 + 5 - 1C_{10} =^{14}C_{10}$

= $14C_{4}$ ($\because\mspace{6mu}^{n}C_{r} =^{n}C_{k},\mspace{6mu} \Rightarrow \mspace{6mu} r + k = n)$