on a game show , a contestant is given 3 keys , each of which opens exactly one of 3 identical boxes . the first box contains $ 5 , the second $ 500 , and the third $ 5000 . the contestant assigns each key to one of the boxes and wins the amount of money contained in any box that is opened by the key assigned to it . what is the probability that a contestant will win more than $ 5000 ?
Choices.
A) 1 / 9  B) 4 / 6  C) 3 / 6  D) 1 / 2  E) 1 / 6

Rationale: let ' s call the boxes that contain $ 5 , $ 500 , and $ 5000 , 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 $ 5000 . 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 $ 5000 , not more than $ 5000 . 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 $ 5000 . 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 : e
Answer: E