How many ways can 6 indistinguishable letters be put into 3 mail boxes?

Answer 1

Here, (x, y, z) means put x letters in the first box, y in the second, and z in the third.

(6, 0, 0)
(5, 1, 0)
(5, 0, 1)
(4, 2, 0)
(4, 1, 1)
(4, 0, 2)
(3, 3, 0)
etc.

Before long, you notice a shortcut and find an easier way to count, as there's 1 possible combination with 6 in the first box, 2 combinations with 5 in the first box, and so on. You conclude from that that if you had 100 letters, you could solve the problem just as easily.

Good work in advance.

Answer 2

distributions are:
6 0 0, 5 1 0, 5 0 1, 4 2 0, 4 0 2, 4 1 1, 3 3 0, 3 0 3
3 2 1, 3 1 2, 2 4 0, 2 0 4, 2 3 1, 2 1 3, 2 2 2, 1 5 0
1 0 5, 1 4 1, 1 1 4, 1 3 2, 1 2 3, 0 6 0, 0 0 6, 0 5 1
0 1 5, 0 4 2, 0 2 4, 0 3 3
or 28 possible ways

Answer 3

1 way