At the grocery store, I bought 4 different items. I brought 3 identical bags, and handed them to the cashier. How many ways are there for the cashier to put the items I bought in the 3 identical bags, assuming he might leave some of the bags empty?
The items are distinguishable, the bags are not
4 items is any bag = 1 way
3 items in one bag, 1 in any other = 4C3 = 4 ways
2 items in one bag , 2 in another = 4C2 / 2 = 3 ways
2 items in one bag , 1 in each of the other two = 4C2 = 6