A Wired Equivalent Privacy (WEP) key is a security code that one must enter in order to access a secure WiFi network. The characters in the key are used from the numbers 0 to 9 and letters from A to F, which gives 16 possibilities for each character of the key. Repeats are allowed, that is, the same letter or number can be used more than once in a key. A WEP key for a WiFi network with 64-bit security is 10 characters long.
a. How many different 64-bit WEP keys can be made by using the given numbers and letters?
b. A specific 64-bit network has a WEP key in which the 2nd, 5th, 8th, and 9th characters are numbers and the other 6 characters are letters. How many different WEP keys are possible for this network?
c. A hacker has determined that the WiFi network mentioned in part b will lock him out if he makes 20,000 unsuccessful attempts to break into the network. What is the probability that the hacker will be locked out of the network?