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

Apr 10, 2016

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 $5 {C}_{N}$ ways.
So, the total number of all possible ways is $\sum 5 {C}_{N}$, N = 0, 1, 2, 3, 4, 5.