MATH SOLVE

2 months ago

Q:
# 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. Answer questions with big number answers as powers or sum of powers (Ex: 15%^7 instead of 170, 859, 375) Strings of length 6. Characters can be special characters, digits, or letters. Strings of length 7, 8, or 9. Characters can be special characters, digits, or letters. Strings of length 7, 8, or 9. Characters can be special characters, digits, or letters. The first character cannot be a letter 4) Strings of length. Strings of length 6 Characters can be special characters, digits, or letters, with no repeated characters. You will not be able to answer this with as a power or sum or powers) Strings of length 6. Characters can be special characters, digits, or letters, with no repeated characters The first character cannot be a special character.

Accepted Solution

A:

Answer:There are 14 choices for the first character because there are 4 + 10 digits and special characters. There are 40 choices for each of the remaining characters. Putting the choices together by the product rule, the total number of strings of length j in which the first character is not a letter is 14·40^(j-1)
14·40^6 + 14·40^7 + 14·40^8 = 14(40^6 + 40^7 + 40^8)IDK