1. This problem involves 8-digit binary strings such as 10011011 or 00001010. How many such strings are there? How many such strings end in 0? How many such strings have 1’s for their second and fourth digits? How many such strings have 1’s for their second or fourth digits?

Q10. A ternary string is an ordered string of characters which consists of digits (0,1, or 2). For example, the ternary string 2122010 consists of exactly 2 zero's, 2 one's and 3 two's; another ternary string meeting these conditions is 0021221. How many ternary strings are there with exactly 4 zero's, 2 one's and 6 two's?

Solve the following problems: (a) How many ways can a store manager arrange a group of 1 team leader and 3 team workers from his 25 employees? (b) A state's license plate has 7 characters. Each character can be a capital letter (A – Z), or a non-zero digit (1 – 9). How many license plates start with 3 capital letters and end with 4 digits with no letter or digit repeated? (c) How many binary strings of length 5 have at least 2 adjacent bits that are the same ("00" or "11") somewhere in the string?

How many different passwords are there that contain only digits and lower-case letters, subject to the restrictions that the password must be 6 characters long and contain at least one digit. Your answer can be a single number or a formula with numbers filled in.