The vast majority of Visa and Discover Card credit cards have 16-digit card numbers. The first digit is either 4 (Visa) or 6 (Discover), digits 2 through 6 identify the issuer, digits 7 through 15 identify the customer, and the last digit is a "check digit" determined by the digits that precede it.† Your company, CreditXplosion, Inc., issues both Visa and Discover credit cards.    How many different CreditXplosion Discover card numbers are possible in which the check digit is wrong?

Q: A new committee is to be made from the 8 members of city council. Each member can choose to be on…

A: We have to find nom of committee possible.

Q: A software company employs 9 sales representatives and 8 technical representatives. How many ways…

A: Solve in the following way

Q: If 5 cards are dealt from a standard deck of cards, how many different ways can three clubs and two…

A:

Q: A pharmaceutical firm wishes to alloc

A: Given, Newspaper Magazine Limitations 1 0 1 0 1 1 500 1000 50,000 50,000 250,000

Q: Ms. Ling has 16 boys and 14 girls in her third-grade class. How many ways can she select 2 boys or 2…

A: Ms. Ling has 16 boys and 14 girls in her third-grade class. We want to find how many ways can she…

Q: Out of a list of 20 colleges, how many ways to schedule the visit of 10 of them (one for each month…

A: Given Information: Total number of colleges = 20 Number of college should visit =10 Number of…

Q: Your 7 digit student identification number is randomly generated.  If the digits cannot repeat, how…

A: Permutation:  The number of ways to arrange all the elements of a set into some sequence or order.…

Q: A license plate is to consist of 4 digits followed by 2  uppercase letters. Determine the number of…

A: Solution-: Given: A license plate is to consist of 4 digits followed by 2  uppercase letters. We…

Q: How many 6 digit telephone numbers can be formed if each number starts with 23 and no digit appears…

A:

Q: There are 20 seniors serving the student council of the Cebu Institute of Technology this year. Of…

A: Solution:  Given : n( Ω)=20 Let, A: 3 senior serving who not served before B : 10 serving in their…

Q: What are the number of ways a license plate can have 7 distinct letters and digits, that must start…

A: The license plate will have four letters and three digits.The license plate must start with a letter…

Q: If the state’s license plates include 2 letters followed by 5 digits (ex. AB 12345), how many…

A:

Q: How many six-digit license plates can be made if no plate begins with 0 or 6

A:

Q: There are 15 qualified applicants for 6 trainee positions in a fast-food management program. How…

A: 15-applicants for 6 trainee positionsNo. of different groupspossible=?

Q: the vast majority of visa and discover credit cards have 16 digit card numbers. the first digit is…

A:

Q: how many ways may they selec

A: Given: If the NCAA has applications from 6 universities for hosting its intercollegiate tennis…

Q: If 15 people start a race, in how many different ways can the top 3 finishers be determined?

A: Permutation:   It  is an arrangement of objects in a definite order where the order is important.…

Q: A credit card company gives each of its customers a 4-digit PIN where each digit is selected from…

A: Multiplication rule of counting:If a task consists of a sequence of choices in which there are ‘a’…

Q: You have an ID number containing from 9 digits. How many IDs get the 1. number "6" as their second…

A:

Q: How many 4-digit numbers are there?   And if repetition of digits is not allowed?

A: Given that n= number from 1 to 9 = 9 r = 4 ( since we have to take 4 digit number)

Q: 1, 3, 6, 10, 15, 21, }1 1, 4, 9, 16, 25, 36, ?,? ® 1, 2, 4, 8, 16, 32, ?, ?

A:

Q: The employees of a company are given a 4-digit identification number. How many different numbers are…

A: GivenThe employees of a company are given a 4-digit identification numberNo.of digits from 0-9=10

Q: Find the frst and second dervatives

A: We need to find first and second derivative.

Q: How many 5-number license plates can be made using the digits: 0, 1, 2, 3, 4, 5, if repetitions are…

A: Given that 5-number license plates that are made using digits 0, 1, 2, 3, 4, 5. We have to determine…

Q: Suppose that 175 heads and 225 tails resulted from 400 tosses of a coin. Does this appear to be a…

A:

Q: A social security number contains nine digits such as 074-66-7795. How many different social…

A: The social security number contains nine digits. The digits are choosen from the set {0, 1, 2, 3, 4,…

Q: A grocery pick-up service has 12 appointment openings one morning. If 8 customers have signed up…

A: Combinations: It defines the number of possible ways an object can be selected from a group. In…

Q: A. How many 3 digit numbers greater than 200 can be made from 0,1,2,3,4,5 if repetition of digits is…

A:

Q: At Southwestern Oregon Community College, a committee is being formed to decide on what kinds of…

A: Total number of aspirants = 15 Number of spots = 5

Q: A new employee has a choice of 5 health care plans, 3 retirement plans, and 2 different expense…

A: Introduction: According to the combination rule, if r distinct items are to be chosen from n items…

Q: 4. Evaluate (²52³Vl-Pax

A:

Q: Explain why in a group of 20 people there must be at least two people who share the same birth…

A: There are total 12 months in a year.  So if each person has a distinct birth month, then we can have…

Q: formed from the digits 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9 if repeti

A:

Q: ************ 2. Construct S( 1,3) XP,

A: The cartesian product of A and B is defined by VA×B=VA×VB and the edge set is defined by a1,b1 is…

Q: There are 15 persons in a party and if each 2 of them shakes hands with each other, how many ways…

A: Given data: 15 persons in a party Each 2 of them shakes hands with each other

Q: How many 5-digit license plate numbers can we generate from the numbers, 0, 1, 2, 3, and 4 if it…

A: Given: There are 5digits 0 , 1 , 2 , 3 , 4 We need to count number of  5 digit number plates…

Q: There are 12 eligible students where a delegation of 4 students is selected each year from a college…

A:

Q: At Southwestern Oregon Community College, a committee is being formed to decide on what kinds of…

A:

Q: How many 3 digit numbers may be formed from the digits 0,1,2,3,4, & 5 if no digit may be repeated…

A: We have to form 3 digit numbers which are less than 330 using the digits 0, 1, 2, 3, 4 and 5. Let…

Q: A social security number has 3 digits, then 2 digits, then 4 digits.  If the first 3 digits can’t be…

A: To determine: Different possible cards can be made. Given data: A social security number has 3…

Q: A license plate is to consist of 4 digits followed by 5 uppercase letters. Determine the number of…

A: Digits : 0,1,2,3,4,5,6,7,8,9 Odd : 1,3,5,7,9 Odd = 5 options  Odd = 4 options 8 options 7 options…

Q: There are 100 people waiting in line for IDs.  Of these, 50 are from Indiana, 45 are freshman, and…

A: To count the number of persons satisfying the given conditions

Q: There are 100 students waiting in line to get student IDs. Of these, 50 are from Indiana, 45 are…

A: There are 100 students waiting in line to get student IDs 50 are from Indiana 45 are freshmen 20 are…

Q: Find the combinations of 5-card poker hands containing an ace of diamonds and at least 1 spade card

A:

Q: In a certain state, license plates each consist of 3 letters from the English alphabet, followed by…

A: There are 26 letters (A-Z) in the English alphabet and 10 digits (0-9).   Use the fundamental…

Q: Owners of a restaurant advertise that they offer 1,114,095 different lunches based on the fact that…

A: To explain: How the owner of a restaurant arrive to the number 1,114,095. Given: The owner have 16…

Q: At Southwestern Oregon Community College, a committee is being formed to decide on what kinds of…

A: d) Given that there 10 are women and 5 are men. If the committee consists only of women then we have…

Q: There are 15 qualified applicants for 5 trainee positions in a fast-food management program. How…

A:

Q: How many ten-digit phone numbers can be formed from the digits 0,1,2,3,...,9 if the first digit may…

A: To find: No of ten-digit phone numbers can be formed from the digits 0,1,2,3,...,9 if the first…

Q: A State's License plates consist of 4 letters followed by 5 digits. How many possible license plates…

A: Number of letters = 4 Number of digits = 5 The letters are followed by digits.

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.