Question 907171: Can you please help me with this word problem I do not know where to start.
A bag of Hershey Kisses may contain anywhere from 51 to 57 kisses. How many bags would you need to buy to ensure that you have at least 3 bags with the exact same number of kisses?
Answer by josmiceli(19441)   (Show Source):
You can put this solution on YOUR website! I would call this a problem about
Worst Case Scenarios ( WCS )
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If you are drawing bags from a randomly
mixed barrel of bags, and you draw
7 bags, what is the WCS if you are
looking for 3 bags with the same number
------------------------------------
The WCS is that you draw 51, 52, 53, ... 57
to start with, or, no duplicates at all
-----------------------
But if you draw 1 more bag, you are now
guaranteed 1 duplicate
-----------------------
Each time you pick 7 more bags, you are
guaranteed in a WCS, that you will only
get another duplicate, but not the one
you wanted
-----------------
If you do  picks, then you
are guaranteed 2 of each kind as a WCS
-----------------
On the 50th pick of bags, you are finally
GUARANTEED a WCS of 3 bags with the
same number of kisses
-----------------
An example of a WCS series of 7 picks is:
(1) 51, 52, 53, 54, ... 57
(2) 51, 51, 51, 51, ... 51
(3) 52, 52, 52, 52, ... 52
(4) 53, 53, 53, 53, ... 53
.
.
.
(7) 57, 57, 57, 57, ... 57
------------------------
Note that you don't have 3 that
are the same yet, but 1 more
pick guarantees that you will
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So, you need to pick 50 bags
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