6. Passwords are composed from lower- and uppercase letters of the English alphabet,digits and 34 special...

6. Passwords are composed from lower- and uppercase letters of the English alphabet,digits and 34 special characters. What is the exponential generating function of the sequence an=number of passwords with at least one capital letter, one number and one special character.

Expert Solution

Colby Messinger answered 1 year ago

The English alphabet has 26 letters. There are 6 vowels. (a, e, i, o, u, and...

The English alphabet has 26 letters. There are 6 vowels. (a, e, i, o, u, and sometimes y). Suppose we randomly select 8 letters from the alphabet without replacement. Let X = the number of vowels chosen (including y as a vowel). a. How many possible ways are there to select the 8 out of 26 letters (order does not matter) without replacement? b. What is the probability that X = 2 c. What is the probability that X=1? d....

In the game of ScrabbleTM, the letters of the English alphabet are inscribed on tiles

In the game of ScrabbleTM, the letters of the English alphabet are inscribed on tiles and a prescribed number of tiles are provided for each letter. Consider an ensemble of ScrabbleTM tiles with a probability distribution defined by the frequency of tiles in the box. Explain how to calculate the information entropy of this ensemble. It is not necessary to actually Compute the entropy, but you can if you wish.

(a) How many passwords can you make with 8 characters using Uppercase, Lowercase, digits using at...

(a) How many passwords can you make with 8 characters using Uppercase, Lowercase, digits using at least one Uppercase, at least one Lowercase and at least one digit? (b) How many numbers between 1 and 1,000,000 (inclusive) are divisible by at least one of 3,4 and 5? (c) How many numbers between 1 and 1,000,000 (inclusive) are divisible by at least one of 12, 14, 15?

Consider passwords of length 8 using symbols from the set of lower case letters: {a, b,...

Consider passwords of length 8 using symbols from the set of lower case letters: {a, b, c, ..., z}. (a) How many such passwords use the letter p exactly two times and the letter q exactly two times? To illustrate, both akpqbqop and quaqpoop satisfy this condition. Include a brief indication of your strategy. (b) How many such passwords use the letter p exactly once and the letter q exactly once and also have letters arranged so the p is...

A password is a sequence of letters (a–z) and digits (0–9). Findthe number of passwords...

A password is a sequence of letters (a–z) and digits (0–9). Find the number of passwords of length 10 under the constraints in (a), (b) or (c) (three separate problems). Express your answer using factorials and integers, products and ratios of them, and/or sums of such things.(a) There are 3 letters and 7 digits, and at most one ‘9’.(b) There are 6 letters and 4 digits, and no digit occurs twice.(c) No letters are used BUT the first four digits...

A password is a sequence of letters (a–z) and digits (0–9). Find the number of passwords...

A password is a sequence of letters (a–z) and digits (0–9). Find the number of passwords of length 10 under the constraints in (a), (b) or (c) (three separate problems). Express your answer using factorials and integers, products and ratios of them, and/or sums of such things. (a) There are 3 letters and 7 digits, and at most one ‘9’. (b) There are 6 letters and 4 digits, and no digit occurs twice. (c) No letters are used BUT the...

The ASCII lowercase letters are separated from the uppercase letters by 32. Thus, to convert a...

The ASCII lowercase letters are separated from the uppercase letters by 32. Thus, to convert a lowercase letter to uppercase, subtract 32 from it. Use this information to write a program that reads characters from the keyboard. Have it convert all lowercase letters to uppercase, and all uppercase letters to lowercase, displaying the result. Make no changes to any other character. Have the program stop when the user enters a period. At the end, have the program display the number...

Assembly code Write an assembly program that converts all uppercase letters to their corresponding lower cases....

Assembly code Write an assembly program that converts all uppercase letters to their corresponding lower cases. meanwhile all characters that are not upper case letters should remain unchanged. Hint: ASCII: a = 97, z = 122, A = 65, Z = 90 String : "Riders On The Storm - The Doors"

Each of the first 6 letters of the alphabet is printed on a separate card. The...

Each of the first 6 letters of the alphabet is printed on a separate card. The letter “a” is printed twice. What is the probability of drawing 4 cards and getting the letters f, a, d, a in that order? Same question if the order does not matter.

Same topic: 1. Consider all passwords of length 10 made up of numbers, lower-case letters, and...

Same topic: 1. Consider all passwords of length 10 made up of numbers, lower-case letters, and upper-case letters (from the English alphabet). a) If you pick such a password at random, what is the likelihood that it contains exactly 5 lower-case letters? b) If you pick such a password at random, what is the likelihood that it contains at most 9 lower-case letters? 2. Suppose you’re an ornithologist who specializes in American crows (Corvus brachyrhynchos), and you’ve collected data on...

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