Question

In how many ways can 5 letters be mailed if there are 2 mailboxes available?

Answer 1

32

Explanation:

We can mail N letters in one box, and the remaining `5- N` in the other, for N = 0, 1, 2, 3, 4, 5.
We can select N out of 5 in `5C_N` ways.
So, the total number of all possible ways is `sum5C_N`, N = 0, 1, 2, 3, 4, 5.
This sum is 1 + 5 + 10 + 10 + 5 + 1 = 32.