The number of ways in which 16 identical things can be distributed among 4 persons if each person gets at least 3 things, is

Required number = coefficient of x16 in (x3 + x4 + … + x7)4                             = coefficient of x16 in x12 (1 + x + … + x4)                           = coefficient of x4 in 1−x51−x4= coefficient of x4 in 1−x54(1−x)−4= coefficient of x4 in 1−4x5+6x10−…(1−x)−4= coefficient of x4 in (1−x)−4=7C4=4⋅5⋅6⋅74!=35