on a game show , a contestant is given 3 keys , each of which opens exactly one of the 3 identical boxes . 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 . the first box contains $ 4 , the second $ 400 , and the third $ 4000 . what is the probability that a contestant will win more than $ 4000 ? Choose the most appropriate option.
A) 2 / 6 B) 1 / 6 C) 1 / 8 D) 1 / 3 E) 1 / 2

Rationale: let ' s call the boxes that contain $ 4 , $ 400 , and $ 4000 , 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 $ 4000 . 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 $ 4000 , not more than $ 4000 . 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 $ 4000 . 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 : b
Answer: B