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?

Maplesnowy
Feb 18, 2018

#1**+2 **

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

CPhill
Feb 18, 2018

#4**+1 **

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**

Guest Feb 18, 2018

#6**0 **

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???

Guest Feb 18, 2018