Question 1: How many different passwords contain only digits and lower-case letters and satisfy the given restrictions? Digits ={0,1,2,3,4,5,6,7, 8, 9} Letters = {a, b, c,d, e, f, g, h, i, j,k,l, m,n, 0, p, q, 1, s, t, u, v, W, x, y, z} a. Length is 8 and the password must contain at least one digit. b. Length is 8 and the password must contain at least one digit and at least one letter. Question 2: An employee of a grocery store is placing an order for soda. There are 6 varieties of soda, and they are sold in cases. Each case contains all the same variety of soda. The store will order 15 cases total. a. How many ways are there to select these 15 cases from 6 varieties? b. How many ways are there to select these 15 cases if the employee orders at least 1 of each variety? Question 3: A man is distributing his coin collection with 21 coins to his three children. How many ways are there to distribute the coins if: a. The coins are all the same. b. The coins are all distinct. . The coins are all distinct and each child gets the same number of coins. Question 4: Count the number of strings of length 8 over the alphabet {a, b, } subject to each of the following restrictions. a. The first or the last character is a. b. The string contains at least 7 consecutive b's . The string contains at least 7 consecutive identical characters. Question S: How many ways are there to permute the letters in each of the following words? a. APPLE (Calculate a numerical value) b. SUBSETS (Calculate a numerical value) c. NUMBER d. DISCRETE