Permutations Question Please Show me The explanation for reaching your answer?

Question

In how many ways can five letters be mailed if there are two mailboxes availiable

Answer 1

Taking into account that you ARE using both mailboxes,
Box A - 1.............Box B - 4.
Box A - 2...............Box B - 3.
Box A - 3...............Box B - 2
Box A - 4...............Box B - 1.

BUT, if you choose only 1 box in which to post them all,
it could be:

Box A - 5...............Box B - 0
Box A - 0...............Box B - 5.

That's 4 using both mailboxes, or, 6 if you want to count the
five in A or five in B system.

I would say 4 ways, myself.