A job interviewer has set 10 questions with four answer options and one correct answer. In how many ways can a potential job applicant answer the questions if the applicant may leave any number of questions unanswered?

Q: A volleyball team will be dispatched from a school. If the current volleyball club has 10 members,…

A: A volleyball team has 6 members . Here, there are 10 members in club and we need only 6 of them.

Q: A restaurant offers 20 appetizers and 40 main courses. In how many ways can a person order a…

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

Q: There are 8 boys and 7 girls in the debate team at Central High School. In how many ways can a…

A: We have 8 boys and 7 girls in the debate team.  We need to make a team consisting of 4 members, such…

Q: How many license plates consisting of three letters followed by three digits contain no letter or…

A: Here we have to find  out the combination of licence plate where repetition  of  letters and digits…

Q: From a club of 25 people, in how many ways can a group of six members be selected to attend a​…

A: In how many ways a group of six members can be selected from a club of 25 people.

Q: Apple decided to give an apple watch to the first person in line, an iPhone to the second person in…

A: From the given information, Apple decided to give apple product to all three persons who stand up in…

Q: If a girl has 6 skirts, 10 blouses, and 8 pairs of shoes, how many different skirt-blouse-shoe…

A: We need to find the number of total outfits in given situation.

Q: If a person can select five books from a list of ten, how many different combinations are there?

A: Given data: The total numbers of books are n=10. The number of books selected is r=5. The expression…

Q: From a club of 17 people, in how many ways can a group of six members be selected to attend a…

A:

Q: A softball league has 13 teams. If every team must play every other team once in the first round of…

A: We are given that there are 13 teams and every team needs to play against every other team. For exam…

Q: If 6 persons are to be seated in round table with 6 chairs, how many ways can they be seated?

A:

Q: A combination lock uses 3 numbers, each of which can be 0 to 31. If there are no restrictions on the…

A: Permutation and combination used to calculate the number of possible ways to arrange or select a…

Q: A man has 3 different pairs of shoes, 8 different pairs of socks, 4 different pairs of slacks, and 2…

A: We have given that 3 different pairs of shoes 8 different pairs of socks  4 different pairs of…

Q: A New club at Arvin High has 22 members. In how many ways can the club elect a president and Vice…

A: The number of members in the club is 22. The number of ways of electing a president is C122=22.…

Q: In a recent survey of 100 students, 38 said that they took a Math class as a freshman, 49 said that…

A: Follow 2nd step.

Q: A survey of 800 households revealed that 300 had only a TV, 200 had only a computer, and 100 had…

A: Given that, A survey of 800 household revealed that, 300 had only a computer and 100 had neither a…

Q: From the deck of 52 playing cards, how many ways can 2 cards be drawn such that one is face card and…

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: In how many ways can 5 men and 5 women be seated at a round table if each woman is to be  between…

A: We have round table and 5 men and 5 women be seated at round table if each women is to be between…

Q: An equestrian club has seven members. If the club wants to select a president, vice president, and…

A:

Q: An ice cream store sells two drinks in four sizes and has five flavor add ons. In how many ways can…

A: From the provided information, The ice cream store sells two drinks in four size and has five flavor…

Q: If there are 10 multiple-choice questions on an exam, each having three possible answers, how many…

A: From the provided information, There are 10 multiple-choice questions on an exam. Each question has…

Q: A state makes license plates with two letters followed by four numbers. if no repetitions of the…

A: The license plates must consist of two letters followed by four numbers.

Q: Suppose you have a set of cups and saucers which are red, orange, green, light blue, dark blue, and…

A: Number of different coloured coffee cup=6 Number of different coloured saucer=6

Q: A restaurant offers 4 appetizers and 6 main courses. In how many ways can a person order a​…

A: One object from m objects can be selected in mP1 ways.

Q: A girl has 9 skirts, 4 blouses, and 6 pairs of shoes. How many different skirt-blouse-shoe outfits…

A: 5) Given that the girl has 9 skirts, 4 blouses and 6 pairs of shoes. Total number of ways 9+4+6=19…

Q: There are 10 doors to a coliseum. In how many ways can a person go in and out if one can enter any…

A: There are 10 doors to a coliseum . A person can go in in 10 ways.

Q: A combination lock uses 4 numbers, each of which can be 0 to 36. If there are no restrictions on the…

A: Here, it can be observed that all numbers are independent of each other.

Q: A restaurant has on its menu four fish dishes, two potato dishes, and two green vegetables. In how…

A: Giventhe total number of fish dishes = 4the total number of potato dishes = 2the total number of…

Q: A woman has two skirts and six blouses. Assuming that they all match, how many different skirt and…

A: As we know, nCx=n!(x)!  *  (n-x)! ; where n!=1*2*3*.....(n-1)*n

Q: How many 5-card hands are possible from a standard deck of 52 playing cards if the cards are drawn…

A: How many 5-card hands are possible from a standard deck of 52 playing cards if the cards are drawn…

Q: A phone number in the United States consists of 10 digits, 3 for a area code and 7 for the phone…

A: Given Data: The number of digits whole phone number consists of: 10 digits The number of digits the…

Q: A restaurant offers 8 entrees and 9 desserts. In how many ways can a person order a two-course meal?

A: We can find the answer as below.

Q: How many license plates can be made using either two or three letters followed by either two or…

A:

Q: A college has 3 entrance gates and 2 exit gates. In how many ways can a student enter then leave the…

A:

Q: In how many ways can 5 boys and 4 girls be arranged on a bench if there is no restriction? How about…

A:

Q: There are 25 people in a club. In how many ways can the club elect a president, a secretary and a…

A:

Q: A license plate consists of two letters and three digits. How many different plates can be made if…

A: no.of digits (0 to 9)=10no.of letters (A to Z)=26

Q: A sub sandwich shop offers 22 toppings to choose from. How many ways could a person choose a…

A: Given problem:- A sub sandwich shop offers 22 toppings to choose from. How many ways could a person…

Q: If there are three candidates for governor and five for mayor, in how many ways can the two offices…

A: We have given that  Candidates for governor = 3 Candidates for mayor = 5 Total candidates = 8

Q: A man has eight shirts and five ties. Assuming that they all match, how many different shirt-and-tie…

A: Given,            A man has eight shirts and five ties.

Q: A student has to answer 8 questions, choosing at least 4 questions from each of parts A. If there…

A: Given,no.of questions in part A=6no.of questions in part B=7

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: How many license plates are possible consisting of 4 letters followed by 3 digits if the first…

A: The license plate consists of 4 letters followed by 3 digits. Thus, it has 7 places to fill up.…

Q: A Maryland automobile license plate consists of three letters followed by three numbers.  How many…

A: As per bartleby guidelines only one question should be answered once, please upload each question…

Q: If you pick 4 cards without replacement from a standard deck of 52 cards, how many different…

A:

Q: As a television executive, you have been given 8 shows to choose from to run during your prime time…

A: Total number of shows available = 8 Available time slot = 6

Q: If a club consists of 12 members, how many different ways are there for the club to fill the…

A: Given,total members=12

Q: If there are 10 people and only 6 chairs are available, in how many ways can they be seated?

A:

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.