Question

Problem 1 (12 points): In this problem you will count the number of passwords with certain characteristics. The characters in the passwords are all either letters or digits. You can assume all letters are lower case, so there are only 26 letters. State how many passwords there are with the given restrictions: 1. Length is 6 or 7 2. Length is 6 and it must contain at least one digit. 3. Length is 6 and it must have at least one digit and one letter. 4. Length is 6 and it can not start with a digit.

Answer 1

369363364367 1) the passwords are all either letters (on digits. as the letters are only lower lase = 26 S and no. of digits = 10 36 if length = 6 then no. of passwords passwords are to be = (3696 = 2,176,782,336. if length=7 the no. of passwords are to 'be = (36)7 : as the repetitions are allowed. Hence the . above are the answers. 2 length is 6 and Contain atleast one digit Here we first find' with no digits. as there no digits = 26. rio passwords possible-- (26)*: i at least one digit - total no fa posswords- no of passwords with letters only = (36)6 - (2616, := 1,867, 866, 5600 ③ length is ab and one digit and one letter. Hence total no. of passwords - no of passwords with letters only- no. of posswords with digitsonly ne no. of Passwords with one digit and One letter atleast. Scanned with CamScanner

| 4) ) (35) - {at) (isss ) 1, 6s, sbs, 55 length is "6" Cannot start with a digit ITE ㅋ 26 x (36) Ciros a letters = 25 - lefess + digits = 36) = 1,572,120,576 CSScanned with CamScanner