Distribution of Identical Objects

Firstly, we can give one orange to each child. There are four children. So, the remaining oranges now are 16 - 4 = 12. 

Now we distribute 12 oranges among 4 children with no restriction.

We can directly apply the formula here, i.e. n things can be distributed among r candidates in $$^{n+r-1}C_{r-1}$$ ways. 

Here, n = 12 and r = 4

Applying the formula, we get: $$^{12+4-1}C_{4-1}=^{15}C_3=\frac{15\times14\times13}{3\times2\times1}$$ = 455