A database uses 20-character strings as record identifiers. The valid characters in these strings are upper-case...

A database uses 20-character strings as record identifiers. The valid characters in these strings are upper-case letters in the English alphabet and decimal digits. (Recall there are 26 letters in the English alphabet and 10 decimal digits.) How many valid record identifiers are possible if a valid record identifier must meet all of the following criteria:

Letter(s) from the set {A,E,I,O,U} occur in exactly three positions of the string.
The last three characters in the string are distinct decimal digits that do not appear elsewhere in the string.
The remaining characters of the string may be filled with any of the remaining letters or decimal digits.

Expert Solution

Colby Messinger answered 1 year ago

For this question, a block is a sequence of 20 characters, where each character is one...

For this question, a block is a sequence of 20 characters, where each character is one of the 26 lowercase letters a-z. For example, these are blocks: iwpiybhunrplsovrowyt rpulxfsqrixjhrtjmcrr fxfpwdhwgxtdaqtmxmlf How many different blocks are there? A block is squarefree if no character appears two times consecutively. The first and third example above are squarefree, but the second example is not because of the two consecutive occurrences of r. How many squarefree blocks are there? A block is non-local if...

2. Non-Local Strings For this question, a block is a sequence of 20 characters, where each...

2. Non-Local Strings For this question, a block is a sequence of 20 characters, where each character is one of the 26 lowercase letters a-z. For example, these are blocks: iwpiybhunrplsovrowyt rpulxfsqrixjhrtjmcrr fxfpwdhwgxtdaqtmxmlf How many different blocks are there? A block is squarefree if no character appears two times consecutively. The first and third example above are squarefree, but the second example is not because of the two consecutive occurrences of r. How many squarefree blocks are there? A block...

A computer system uses passwords that contain exactly 5 characters, and each character is 1 of...

A computer system uses passwords that contain exactly 5 characters, and each character is 1 of the 3 lowercase letters (a, b, c) or 3 upper case letters (A, B, C) or the 5 odd digits (1, 3, 5, 7, 9). Let Ω denote the set of all possible passwords, and let A and B denote the events that consist of passwords with only letters or only integers, respectively. Determine the probability that a password contains at least 1 uppercase...

A computer system uses passwords that contain exactly six characters, and each character is 1 of...

A computer system uses passwords that contain exactly six characters, and each character is 1 of the 26 lowercase letters (a–z) or 26 uppercase letters (A–Z) or 10 integers (0–9). Let Ω denote the set of all possible passwords, and let A and B denote the events that consist of passwords with only letters or only integers, respectively. Determine the number of passwords in each of the following events. (a) Password contains all lowercase letters given that it contains only...

Think of a password 8 character long which uses at last one lower-case letter, one capital...

Think of a password 8 character long which uses at last one lower-case letter, one capital letter, and one number, but uses none more than once. What's your password? How many possible permutations are there for an 8 character password which meets those criteria? How many fewer combinations without regard to order are there for an 8 character password which meets those requirements. How would you calculate how many permutations there are for an 8 to 12 character password which...

Question