there are 11 identical balls to be placed in 3 bags such that sum of no. of balls in 2 bags is greater than no. of balls in other bag.in how many ways

ans is 15

let x,y and z be no. of balls in 3 bags

x+y+z=15

min. of x/y/z is 1 and max. is 5

→  1 ≤ x,y,z ≤ 5

hence no. of ways of req. distribution is co-eff of x¹¹ in (x+x²+x³+x⁴+x⁵)³

→ co-eff of x⁸ in (1+x+x²+x³+x⁴)³ = 15