A computer system uses passwords that are exactly seven char

A computer system uses passwords that are exactly seven characters and each character is one of the 26 letters (a-z) or 10 integers (0-9). Uppercase letters are not used. Answer the following questions under two different scenarios, [1]-the characters can be duplicated (used more than once in the same password), [2]-the characters can be used once. How many passwords are possible? lf a password consists of exactly 6 letters and one number: In how many ways the number can be positioned in the password? How many passwords are possible? lf a password consists of 5 letters and two numbers, how many passwords are possible? In how many ways the two numbers can be positioned in the password? How many passwords are possible? Generate a function that gives the number of possible passwords formed by n characters with i letters and j numbers (I + j = n, and n = l, 2 ,3....) What is the probability to guess a password when you are given all its 7 characters (not ordered)? What is the probability to guess a password that has only two missing characters?

Solution

if can be duplicated

36*36*36*36*36*36*36 = 7.836x10 ^10

if can\'t be duplicated

36*35*34*33*32*31*30 = 4.207x10^10

2)

IN 7 POSITION DIFFERENTS

can be duplicated

there are 26*26*26*26*26*26*1 = 308915776*7=2162410432

can\'t be duplicated

26*25*24*23*22*21*1 = 165765600*7=1160359200

3)

there are 6 ways that the 2 numbers can be positioned in the password

can be duplicated

26*26*26*26*26*10*10 = 1188137600 * 6 =7128825600

cant be duplicated

26*25*24*23*22*10*9 = 710424000*6= 4262544000

for the other literals

I can gladly help you but you should post it in a new question