Dropping letters in post boxes In how many different ways can 5 letters be dropped in 3 different post boxes if any number of letters can  be dropped in all of the post boxes?

In general number of droppings of $k$ letters in $m$ boxes is
$$\sum_{x_1+x_2+...+x_m=k,0\leq x_i\leq k}1=\binom{m+k-1}{k}$$
in our case $m=3,k=5$
$$\sum_{x_1+x_2+x_3=5,0\leq x_i\leq 5}1=\binom{5+3-1}{5}=21$$
Below is the list of all droppings
$$(5,0,0),(0,5,0),(0,0,5)$$
$$(4,0,1),(4,1,0),(0,1,4),(0,4,1),(1,0,4),(1,4,0)$$
$$(3,1,1),(1,3,1),(1,1,3)$$
$$(2,3,0),(2,0,3),(3.0,2),(3,2,0),(0,2,3),(0,3,2)$$
$$(2,2,1),(2,1,2,(1,2,2)$$
