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 are not all the same AND the last four digits are not all the same, AND the 4th, 5th, 6th and 7 digits are not all the same.

Expert Solution

a) P = P(with zero 9) + P(with one 9)

= 10C3(26)3(9)7 + 10C3(26)3(9)6 Answer

b) P = 10C6(26)6(10*9*8*7) Answer

(Here first we selected 6 places out of 10 for alphabets, then assigned alphabets to those places, then placed the four digits)

c) P = P( Making a password from digits) - P(Making a password from digits only, and first four are same, next four are same and the last four digits are same)

= (10)10 - (10)3 Answer

orchestra answered 2 years ago

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...

In an exactly 8 character long password where capital letters, small letters, and digits (0 to...

In an exactly 8 character long password where capital letters, small letters, and digits (0 to 9) must be used. Regardless of the order, how many passwords will use exactly 5 ones, 4 twos, and one Z?

A random number generator produces a sequence of 18 digits (0, 1, ..., 9). What is...

A random number generator produces a sequence of 18 digits (0, 1, ..., 9). What is the probability that the sequence contains at least one 3? (Hint: Consider the probability that it contains no 3's. Round your answer to four decimal places.)

For 3 digits password. a). Find all possible outcomes of 3 digits of 0-9 numbers with...

For 3 digits password. a). Find all possible outcomes of 3 digits of 0-9 numbers with no repetition allowed b). Find all possible outcomes of 3 digits of 0-9 numbers with repeition allowed but no more than two repetition c). Find all possible outcomes of 3 digits of 0-9 for repetition numbers only. d) Find all possible outcomes of 3 digits of 0-9 for repeition numbers only but no more than 2 repetition. e). Find all possible outcomes of 3...

You need to create a four-digit password using 0-9. How many passwords are possible, without repeating...

You need to create a four-digit password using 0-9. How many passwords are possible, without repeating a number, if a password must not start with a 0?

Password consists of five characters: one lowercase letter and four digits 0 – 9. How many...

Password consists of five characters: one lowercase letter and four digits 0 – 9. How many possible combinations for the password are there if digits can be repeated? How many possible combinations for the password are there if digits can not be repeated? What is a percentage of passwords with repeated digits?

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.

A password is a sequence of five characters. Each character is one of twenty-six uppercase letters...

A password is a sequence of five characters. Each character is one of twenty-six uppercase letters (“A” through “Z”), one of ten digits (“0” through “9”), or one of five symbols (“+”, “-”, “!”, “<”, “>”). Count the number of possible passwords that can be created in each of the following scenarios. Consider each part of this questions separately. (a) There are no restrictions on how the characters are chosen. (b) A password must begin with a letter and end...

A seqstring is a sequence of 18 letters(one of the 26 lowercase letters a-z). How many...

A seqstring is a sequence of 18 letters(one of the 26 lowercase letters a-z). How many seq strings are there where the number of letters between any two occurences of the same letter is at least 2?

Find the number of passwords that use each of the digits 3,4,5,6,7,8,9 exactly once. IN how...

Find the number of passwords that use each of the digits 3,4,5,6,7,8,9 exactly once. IN how many of the passwords: 1. are the four odd digits consecutive? 2. are no two odd digits consecutive? 3. are the first three digits even? 4. are the three even digits consecutive?

Question