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The Million Dollar Suitcase - A Puzzle

Sometime back, I encountered a puzzle posted by a member in a LinkedIn group. It was called a Million Dollar Suitcase. A scenario with a challenge was described and we had to find a solution. It went like this:
Three suitcases are all labeled incorrectly, and you must get the labels right in order to find the million dollar suitcase (the one full of hundred dollar bills). 
The labels on the suitcases read as follows:
  • $100 Bills
  • $1 Bills
  • Both ($100 & $1 Bills)

You are allowed one test. You may remove only one bill from a single suitcase, after which you must make your determination. You can’t peek into the suitcases. Can you find the million dollar suitcase?

The Solution

I read about it and devised a solution before checking it out on the site. My explanation was:
Assuming all of the suitcases are definitely mislabeled - we can safely remove one (i.e. the $100 suitcase) from the game and consider only two suitcases: $1 and Both. 
If we select the one labeled "$1" for examination, we have half a chance to get into some trouble. If the bill you remove from the "$1" suitcase is actually $1, then we are saved, since it obviously is both. But if happens to be $100, we have no way of confirming if it is actually the "$100" suitcase or the "Both" case. 
Therefore, we go directly to the suitcase labeled "Both". It can only have two types of bills - either all $1 or all $100. So, when we remove a bill and find it to be $1, then we pounce on the suitcase labeled $1 and run for it. It it is $100, then we just got ourselves a million dollars! :-) 
However, all of this based on the presumption that none of the suitcases are what they are actually labeled to be. If there is any chance that even one of the cases may actually be what the label says, then this method won't do.  
And this solution turned out to be correct! :-)

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