Question

The number of ways in which 10 apples can be distributed among 5 persons if each person can get any numbers of apples is

• A. $14C_{4}$
• B. $14C_{5}$
• C. $14C_{6}$
• D. None of these

Answer 1

Answer: (A)

$14C_{4}$

Answer 2

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

= Coefficient of x¹⁰ in $\left( \frac{1}{1 - x}(1 - x^{11}) \right)^{5}$

= Coefficient of x¹⁰ in (1-x)^-5 = $14C_{4}$