OBX Cart Rentals has created a website for customer access. They are trying to determine a reasonably secure number of available passwords. They have decided to allow upper case letters, lower case letters, digits (0 â 9), and the three special characters: $, ! ?. Find the number of possible 6 character passwords given each of the conditions (Note: you MUST simplify completely.) a. The password must begin with a letter (either upper or lower case)
i. repetitions permitted
ii. repetitions not permitted
b. The password must begin with a letter and end with a special character ($, !, ?):
i. repetitions permitted
ii. repetitions not permitted

A)

i) for repetitions

there will be : 52 * 65 * 65 * 65 * 65 * 65 = 60335112500 number of passwords

ii) for Non - repetitions

there will be : 52 * 64 * 63 * 62 * 61 * 60 =  47576954880

B)  

i) for repetitions

there will be : 52 * ( 65 )^4 * 3  =  2784697500

ii) for Non-repetitions

there will be : 52 * 63 * 62 * 61 * 60 * 3 = 2230169760

Step-by-step explanation:

Total Number of letters = 52

Number of upper case letters = 26

Number of lower case letters = 26

Number of digits ( 0 - 9 ) = 10

special characters = 3

password = 6 characters

Therefore the total number of choices = 52 + 3 + 10 = 65

A) The password must begin with a letter (either upper or lower case)

i) for repetitions

there will be : 52 * 65 * 65 * 65 * 65 * 65 = 60335112500 number of passwords

ii) for Non - repetitions

there will be : 52 * 64 * 63 * 62 * 61 * 60 =  47576954880

B)  The password must begin with a letter and end with a special character ($, !, ?):

i) for repetitions

there will be : 52 * ( 65 )^4 * 3  =  2784697500

ii) for Non-repetitions

there will be : 52 * 63 * 62 * 61 * 60 * 3 = 2230169760

answer: 2x + 2 − 2 = 10 − 2; subtraction property of equality

step-by-step explanation: