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GMAT Practice Question (One of Hundreds)

Superior Security recently discovered a computer on its network had been hacked. The computer password contained 16 characters (including only numbers and letters). What is the probability that the password to Superior’s hacked computer was correctly guessed on the first try? (Assume that the hacker knew the password contained 16 characters, comprised only of numbers and both lower-case and upper-case letters.)

A)	52!/(16!36!)
B)	1/[62!/(16!46!)]
C)	1/[52!/(16!36!)]
D)	1/5216
E)	1/6216

Correct Answer: E

For each of the 16 characters that form the password, the possible characters include: 26 lower case characters, 26 upper case characters, and 10 digits.

1. The probability of guessing correctly on the first try is 1 divided by the number of pass permutations (i.e., unique arrangements of passwords). For example, if there were four possible password combinations, the probability of guessing the password correctly on the first try would be 1/4
2. For each of the 16 characters that form the password, the possible characters include: 26 lower case characters, 26 upper case characters, and 10 digits. So, for each character in the password, there are 62 possible characters.

   Character 1	Character 2	Character 3	...	Character 15	Character 16
   62 possibilities	62 possibilities	62 possibilities	62 possibilities	62 possibilities	62 possibilities

3. Since there are 16 characters in the password and each character could be one of 62 possibilities, there are a total of 62¹⁶ unique password permutations (i.e., there are 62¹⁶ different possible passwords, only one of which is the correct password). So, the probability of guessing the password on the first try is 1/62¹⁶.

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