Suppose that you have just arrival at Rutgers and must select a password for you

Question

Suppose that you have just arrival at Rutgers and must select a password for your Scarlet Mail account. Assume that letters are case sensitive, i.e. lower case and upper case letters are considered different. In each part of this problem (a through c). there is a different rule imposed by Rutgers for how you must form your password. For each of these four different rules for forming passwords, there are two questions you must answer how many different possible choices do you have for your password, and once you have selected your password, if someone knew the rule for forming passwords and tried to guess your password (at random), what Would be the probability of guessing yours correctly. The password must consist of exactly 12 letters, but adjacent characters must be different from one another. The password must consist of exactly 12 letters, with no repetition of letters allowed, i.e once a letter has been used, it cannot be used again. The password must consist of exactly 12 or 13 or 14 letters, with no repetition of characters allowed.

Explanation / Answer

a) number of ways to make the password =first letter can be any of 52 letters, second letter should be one except the previous one cause it should not be same as previous chosen because of adjacent rulehence it must have 51 choices for third again we have 51 choices and so on

=52*(51)11 =3.157*1020

probabilty of guessing the password =1/(3.157*1020)=3.1676*10-21

b) total numbe of passwords if no repetitions are allowed =choosing 12 letters out of 52 and ordering them

=(52)12 =52!/(40)! =9.8856*1019

probabilty of guessing the password =1/(9.8856*1019)=1.01157*10-20

c)total numbe of passwords if no repetitions are allowed of 12,13,14 letters ==(52)12 +(52)13 +(52)14 =1.54*1023

probabilty of guessing the password =1/(1.54*1023)=6.48*10-24

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