Matt's four cousins are coming to visit. There are four identical rooms that they can stay in. If any number of the cousins can stay in one room, how many different ways are there to put the cousins in the rooms?
I count 35 ways as follows:
4 + 0+ 0 + 0 = 4.........................4 permutations
3 + 1 + 0 + 0= 4........................12 permutations
2 + 2 + 0 + 0= 4..........................6 permutations
2 + 1 + 1 + 0 = 4........................12 permutations
1 + 1 + 1 + 1 = 4.........................1 permutation
Total =4 + 12 + 6 + 12 + 1 =35 ways.
