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# Distinguishability help???

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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?

Feb 18, 2018

#1
+101084
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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

Feb 18, 2018
#2
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Maplesnowy  Feb 18, 2018
#3
+193
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I think it's because the items are distinguishable?

Maplesnowy  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

Feb 18, 2018
#5
+101084
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Thanks, guest...14 is correct....

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???

Feb 18, 2018