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 distinguishability problem

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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?

 Mar 3, 2019

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 #1
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xxxxxxxxxxxx.

 Mar 3, 2019
edited by Guest  Mar 3, 2019
 #2
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The items are distinguishable, the bags are not

 

Enumeration

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

 

14 ways

 

 

cool cool cool

 Mar 3, 2019

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