The number of ways of distributing 15 apples to three persons A , B , C such that A and C each get at least 2 apples and B gets at most 5 apples is

Step-by-step solution

aligned & Required number of ways & = Coeff of x¹⁵ in & (x^2+x^3+x^4+ )^2 (1+x+x^2+x^3+x^4+x^5 ) & = Coeff of x¹¹ in (1-x)⁻² (1-x^6 )(1-x)⁻¹- Coeff of & x¹¹ in (1-x)⁻³ (1-x^6 ) & = 11+3-1 11 - ⁵⁺³⁻¹ C₅= 13 11 - ^7 C₅=57 aligned