n =3 childrens
x1 + x2 + x3 = 2 //apple
r = 2
ways = $_{r}^{n+r-1}\textrm{C}$ = $_{2}^{4}\textrm{C}$ = 6
x1+x2+x3 = 3 // orange
r = 3
ways = $_{r}^{n+r-1}\textrm{C}$ = $_{2}^{5}\textrm{C}$ = 10
x1+x2+x3 = 4 // mango
r = 4
ways = $_{r}^{n+r-1}\textrm{C}$ = $_{4}^{6}\textrm{C}$ = 15
total ways = $6\times 10\times 15 = 900$
Thank you !