1. RANK the following four rules from MOST combinations to LEAST combinations. Explain how you know. (Intuition is good, but math is better!)
Password must be 8 lowercase letters. No numbers.
There are 26 lower case letters, we choose 8, so
C(26,8) = 1562274
Password must be 6 letters but they may be lowercase or uppercase. No numbers.
There are 26 lower case letters amd 26 upper case letters. That's 52 letters.
We choss 6, so
C(52,6) = 20358520
Password must be 4 characters - either uppercase, lowercase, or numbers.
There are 52 upper and lower case letters plus 10 digits, so that's 62
total characters. We choose 4, so
C(62,6) = 61474519
Password must be 10 letters, but each character must alternate between an UPPERCASE letter and a number.
Examples: P6U2P5R6H7, 8E6K9K0P4D
Passwords which begin with an upper case letter:
26*10*26*10*26*10*26*10*26*10 = 1188137600000
Passwords which begin with a digit:
10*26*10*26*10*26*10*26*10*26 = 1188137600000
That's a total of 1188137600000 + 1188137600000 = 2376275200000
2. How many ways are there to rank the options?
The way the problem lists them is from LEAST to MOST,
so reverse them.
Edwin
