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:
https://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
_________________
Mike McGarry
Magoosh Test PrepEducation is not the filling of a pail, but the lighting of a fire. — William Butler Yeats (1865 – 1939)