1) Consider the following definitions for sets of characters: Digits={0, 1, 2, 3, 4, 5, 6,...

 

Transcribed Image Text:

1) Consider the following definitions for sets of characters: 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, o, p, q, r, s, t, u, v, W, X, Y, Z } Special characters = { *, &, $, # } Compute the number of passwords that satisfy the given constraints. (a) Strings of length 6. Characters can be special characters, digits, or letters. (b) Strings of length 7, 8, or 9. Characters can be special characters, digits, or letters. (c) Strings of length 7, 8, or 9. Characters can be special characters, digits, or letters. The first character cannot be a letter. (d) Strings of length 6. Characters can be special characters, digits, or letters, with no repeated characters. (e) Strings of length 6. Characters can be special characters, digits, or letters, with no repeated characters. The first character can not be a special character. 2) How many strings are there over the set {a, b, c} that have length 10 in which no two consecutive characters are the same? For example, the string "abcbcbabcb" would count and the strings "abbbcbabcb" and "aacbcbabcb" would not count. 1) Consider the following definitions for sets of characters: 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, o, p, q, r, s, t, u, v, W, X, Y, Z } Special characters = { *, &, $, # } Compute the number of passwords that satisfy the given constraints. (a) Strings of length 6. Characters can be special characters, digits, or letters. (b) Strings of length 7, 8, or 9. Characters can be special characters, digits, or letters. (c) Strings of length 7, 8, or 9. Characters can be special characters, digits, or letters. The first character cannot be a letter. (d) Strings of length 6. Characters can be special characters, digits, or letters, with no repeated characters. (e) Strings of length 6. Characters can be special characters, digits, or letters, with no repeated characters. The first character can not be a special character. 2) How many strings are there over the set {a, b, c} that have length 10 in which no two consecutive characters are the same? For example, the string "abcbcbabcb" would count and the strings "abbbcbabcb" and "aacbcbabcb" would not count.