1) Before installing a new security system, a home owner intends to assess the r
ID: 3305209 • Letter: 1
Question
1) Before installing a new security system, a home owner intends to assess the reliability of a lock having a digital key which is used in the system. a) if the digital kev is upper case alphanumeric (i.e., it is a combination of upper-case letters and digits), and consists of 7 characters, how many different combinations are possible? b) if the key is case-sensitive alphanumeric, and is 6-characters-long, how many different c) what about the situation when the key is the same as in a) but all the characters must be d) it is known that a certain individual has an ability to try 300 combinations per microsecond combinations are possible? unique? If the homeowner has chosen a key according to a), and if it takes the police 3 minutes to arrive after the first incorrectly entered key, does the homeowner have anything to worry about?Explanation / Answer
a) Each of the 7 characters can be any of the 36 possibilities, 0 through 9 and 'A' through 'Z'.
Therefore, the total number of ways = 36 * 36 * 36 * 36 * 36 * 36 * 36 = 36 ^7 = 78364164096.
b) Each of the 6 characters can be any of the 62 possibilities, 0 through 9, 'a' throgh 'z' and 'A' through 'Z'.
Therefore, the total number of ways = 62 * 62 * 62 * 62 * 62 * 62 = 62 ^6 = 56800235584.
c) The first of the 7 characters can be any of the 36 possibilities, 0 through 9 and 'A' through 'Z'.
The seond character can be any thing otherthan the first character. Therefore, It can be any of the remaining 35 characters.
Similarly, the third character can be an of the remaining 34 characters (excluding the characters used for the first two spots).
Similarly, the fourth character can be an of the remaining 33 characters (excluding the characters used for the first three spots).
Similarly, the fifth character can be an of the remaining 32 characters (excluding the characters used for the first four spots).
Similarly, the sixth character can be an of the remaining 31 characters (excluding the characters used for the first five spots).
Similarly, the seventh character can be an of the remaining 30 characters (excluding the characters used for the first six spots).
Therefore, the total number of ways = 36 * 35 * 34 * 33 * 32 * 31 * 30 = 36p7 = 42072307200.
d) The total number of combinations that can be tried in 3 minutes is 300 * 10^6 * 3 * 60 = 54 * 10^9 which is less than 78364164096 (the total number of combinations possible.) As 54/78 = 0.69, the probability of getting it opened is almost 70 percent. Therefore, whether the owner of the house to be worried or not depends on valuables inside the house which can be stolen in less than 3 minutes.
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