Permutation and combination theory The number of ways of distributing 12 identical oranges among 4 children so that every child gets atleast 1 and no child more than 4 is

Give each child one orange, then distribute the remaining eight so that no child receives more than three additional apples.
Count and add the permutations of each of: $(3,3,2,0), (3,3,1,1), (3,2,2,1), (2,2,2,2)$.

Or simply count and add the permutations of each of: $(4,4,3,1), (4,4,2,2), (4,3,3,2), (3,3,3,3)$.
