+194 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?
+128475
The bags are indistinguishable, so the only thing we have to worry about is the number of ways to partition 4 items
The partitions are
(4,0,0) (3,1,0) (2,2,0) (2,1,1)
We could put all 4 items in one bag = 1 way
We could put 3 items in one bag and 1 in another = 1 way
We could put 2 items in 2 of the bags = 1 way
We could put 2 items in one bag and one item in each of the other two = 1 way
So....4 ways
See the answer here, if you can understand it:
https://www.quora.com/In-how-many-ways-can-4-distinct-balls-be-distributed-into-3-identical-boxes
Bag1 Bag2 Bag3
4 0 0.....................1
3 1 0.....................2
2 2 0.....................3
1 3 0.....................4
0 4 0.....................5
3 0 1.....................6
2 0 2.....................7
1 0 3.....................8
0 0 4.....................9
0 3 1.....................10
0 2 2.....................11
0 1 3.....................12
1 2 1.....................13
1 1 2.....................14
Here is the actual distribution!!!!. Or, did I forget something???
