The serial number on a new twenty-dollar bill consists of two letters followed by nine digits and then a letter. How many different serial numbers are possible, given the following conditions? (a) Letters and digits cannot be repeated. (b) Letters and digits can be repeated. (c) The first and last letters are repeatable vowels, the second letter is a consonant, and the digits can be repeated. (Let y be a consonant)

Q: a) Suppose in a university, each subject offered to students has a subject code consisting of four…

A: a) In a university each subject offered to students has a subject code consisting of four letters…

Q: How many ways can the letters of the word PROMISE be arranged so that the vowels always come…

A: Given word is PROMISENumber of vowels in word PROMISE…

Q: 1)a) How many 3 digits passcodes are there if first digit must be a 1 or 2 ?   b) How many 3…

A: The possible number for passcode is as follows: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 a) if the first digit…

Q: How many ways are there to seat six boys and eight girls in a row of chairs so that no two boys are…

A:

Q: If repetition of digits is not​ allowed, how many four​-digit numbers can be formed using the…

A:

Q: In how many ways can the letters of the word “rhubarb” be arranged so that all of the vowels are…

A: Given that, The letters of the word “rhubarb” should be arranged such that all vowels are together.

Q: A student has a $1 bil, a $5 bill, a $50 bill, and a $100 bill a. If the student must select at…

A:

Q: To use an automated teller machine at a certain bank, you must enter a 4-digit code, using the…

A: This is a type of permutation problem. We want to arrange 1-9 digits in  4 positions with repetition…

Q: A staff number of a BigHit company is composed of 2 non-vowels uppercase alphabets and 3 digit…

A: GivenA staff number of a BigHit company is composed of 2 non-vowelsuppercase alphabets and 3 digit…

Q: To gain access to his account, a customer using an automatic teller machine (ATM) must enter a…

A:

Q: A passcode is to be created from 2 letters, 2 digits, and 2 special characters (consisting of ?,!,…

A: Combination only includes number of ways of selection whereas, permutation includes number of ways…

Q: Computers manufactured by a certain company have a serial number consisting of a letter of the…

A: We can solve the given problem using concept of sets.

Q: . Five-digit-numbers can be formed from the six digits 2, 3, 5, 6, 7 and 0. If repetitions are not…

A:

Q: Allowing (or requiring) users to use numerical digits (including 0) and one of 28 “special…

A:

Q: 2) Allowing (or requiring) users to use numerical digits (including 0) and one of 31 "special…

A: Introduction: Considering the lower- and upper-case alphabets to be two different characters, total…

Q: Standard

A:

Q: License plates in a particular state are to consist of 2 digits followed by 3 uppercase letters. a)…

A: We have to find out the no of possible  license plates using given conditions.

Q: 10. A bank password consists of four letters of the Roman characters (small and capital letters)…

A: SOLUTION:

Q: How many different ways can a club of 25 members fill the positions of president, vice president and…

A: Given: The positions to be filled by the club members are president, vice president, and Secretary.…

Q: (a) In how many different ways can the letters of the word wombat be arranged if the letters wo must…

A: Using permutation we can get the number of ways the letters can be arranged to make words

Q: 1. Frankie has to create a new Virginia Tech password. Suppose Frankie wants his password to be 7-9…

A: The given data is:

Q: a. A fleet of sixteen taxis is to be dispatched to three airports in such a way that three go to…

A: here AS PER GUIDELINES I HAVE CALCULATED FIRST MAIN QUESTION , AS YOU POSTED A AND B TOTALLY…

Q: To use an automated teller machine at a certain​ bank, you must enter a 6​-digit ​code, using the…

A: To find-  Possible 6 digit codes if repetition of digits are permitted.

Q: (a) In a certain country, the car number plate is formed by 4 digits from the digits 1, 2, 3, 4, 5,…

A: (a) The car number is formed by 4 digits from the digits 1,2,3,4,5,6,7,8 and 9 followed by 3 letters…

Q: 1. The license plates for cars in Nova Scotia typically have 6 digits. The first three digits are…

A:

Q: How many ways are there to arrange the letters m, n, o, p, and q such that neither m nor n is…

A: There are 5 letters in m, n, o, p, and q. We can arrange them in 5!= 120 ways   If m is followed…

Q: 5. From the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9, if six-digit numbers are to be formed and…

A: 5) Total number of digits to be used 8 Unit digit can hold any of the 4-digits; 3,5,7,or 9 for an…

Q: How many of the 60 students in a 25-item quiz can have the same score? 2. Apples, bananas, and…

A: The pigeonhole principle can be used to calculate the least number of objects. The pigeonhole…

Q: How many permutations of a 7-digit phone number exist, assuming that numbers may be repeated and any…

A:

Q: 18. A security company requires its employees to have a 7-character computer password that must…

A: We have 7 places which among 5 must be filled by letters and the remaining 2 must be filled by…

Q: 1 How many ways can the letters of the word "PROMISE" be arranged so that the vowels always come…

A: Since the student has posted multiple questions and does not mention any specific question, so we…

Q: Current rules for telephone area codes allow the use of digits​ 2-9 for the first​ digit, and​ 0-9…

A: Given data current rules for telephone area codes allow the use of digits 2-9 for the first digit…

Q: uppercase letters. ​a) How many different license plates can there be in this state if repetition of…

A:

Q: How many different phone numbers can be formed if it must have 7 digits and cannot start with 0 or 1…

A: Given data: phone numbers can be formed if it must have 7 digits and cannot start with 0 or 1 and…

Q: 2. At a certain company, access codes nust pe 4 composed of the 26 lower case letters of the…

A: Let           A=Access codes 4 to 6 symbolsA1=Access codes with 4 symbolsA2=Access codes with 5…

Q: License plates in a particular state are to consist of 3 digits followed by 2 uppercase letters. How…

A: no.of digits=10  (0 to 10)no.of uppercase letters=26   (A to Z) 9 ways fill it (0 , 2, 3...10) 9…

Q: How many 5-digit numbers can be made from the digits 1 to 9 if: a) Repetition of digits is allowed?…

A: Here AS PER POLICY I HAVE CALCULATED FIRST 3 SUBPART ONLY

Q: (a) If repetition of digits is not​ allowed, how many four​-digit numbers can be formed using the…

A: Solution: a. The given digits are 1, 2, 3, 4 and 5. Here, the repetition is not allowed.

Q: 3. How many different 5-digit identification tags can be made a.if the digits can be used more than…

A: Given: Number of digits in an identification code = 5 Total number of digits = 0 to  9 = 10

Q: How many 4-digit pin codes can be made using the numbers 0 up to 9 if repetition is not allowed and…

A: Solution Total number of digits from 0 to 9 = 10

Q: 3. How many different license plates are possible if a state uses (a) Two letters followed by a…

A: (a).We have  (0,1,2,...,9) 10 digits , and 26  letters (A,B,C,.....,Z). Repetitions of digits and…

Q: 16) How many unique license plate numbers can be created made up of 3 letters (26 possible) followed…

A: The places of letters which are 26 possible can have the following pattern as they can not be…

Q: License plates in a particular state are to consist of 2 digits followed by 3 uppercase letters. ​a)…

A:

Q: 11 Given the digits 6, 7, 8, 9, a. How many four number digits can be formed if there's no…

A: Given digits are  6, 7, 8, 9 each parts are solved below.

Q: 3. In how many different ways can the letters of the word 'OPTICAL' be arranged so that the vowels…

A: The word OPTICAL has three vowels O,I and A. Consider these three letters as 1 and the remaining…

Q: -Each student at State University has a student ID number consisting of five digits (the first digit…

A:

Q: To use an automated teller machine at a certain bank, you must enter a 5-digit code, using the…

A: To use an automated teller machine at a certain bank, we have to enter a 5 digit code using digits…

Q: 2. A combination lock has 4 wheels, each labeled with the 10 digits from 0 to 9. (a) How many 4…

A:

Q: A computer system allows user IDs that are six characters long. If only alphanumeric characters are…

A: According to the provided data, the user IDs are six, r characters long. The alphanumeric characters…

Q: 2) Phone numbers consist of a three-digit area code followed by seven digits. If the area code must…

A: Given information- We have given that a phone number consist of a three-digit area code followed by…

Counting Principles

In statistics, the counting principle can be said to be the concept in which the quantity of an item is determined. There can be a single item, or a group of items, or items that are related to each other. In every possible set of items, the quantity of the possible item groups or their sorting measures can be determined with counting principles.