By multinomial theorem, no. of ways to distribute 30 identical candies among four children C1,C2 and C3,C4 = Coefficient of x30 in (x4+x5+....+x7)(x2+x3+....+x6)(1+x+x2.....)2 = Coefficient of x24 in
(1−x4)
1−x
(1−x5)
1−x
(1−x31)2
(1−x)2
= Coefficient of x24 in (1−x4−x5+x9)(1−x)−4 =27C24−23C20−22C19+18C15=430