Hi, there. I'm happy to help with this.

This is a cool question!

Let's call the boxes that contain $1, $100, and $1000, respectively, Box A, Box B, Box C. These are opened, respectively, by Key A, Key B, and Key C.

We want to know the probability of winning more than $1000. Notice that if the distribution of keys is:

Box A = Key B

Box B = Key A

Box C = Key C

then the contestant wins exactly $1000, not more than $1000. The only configuration that leads to winning more than $1000 is:

Box A = Key A

Box B = Key B

Box C = Key C

i.e., getting all three keys correct. That's the only way to be more than $1000. So, really, the question can be rephrased: what is the probability of guessing the order of keys so that each key matches the correct box?

Well, for a set of three items, the number of possible permutations is 3! = 3*2*1 = 6.

Of those 6 possible permutations, only one of them leads to all three keys being paired with the right box. So, the answer is

Probability = 1/6, answer = C

Does that make sense?

Here's another free practice question involving permutations:

http://gmat.magoosh.com/questions/857The question at that link should be followed by a video solution.

Please let me know if you have any other questions.

Mike

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Mike McGarry

Magoosh Test Prep