A professor gives his students 8 essay questions to prepare for an exam. Only 3 of the questions will actually appear on the exam. How many different exams are possible?

Q: On a math exam, students must answer 5 out of 7 questions from Part A and only 2 out of 4 questions…

A: Introduction: Suppose, there are n different objects. Out of the total number of objects, r objects…

Q: the state department of transportation decides to change the plates to have three letters followed…

A: Given query is to find how many plates are possible if three latters followed by two digits.

Q: A student needs 6 more classes to graduate. If she has met the prerequisites for all the classes,…

A: The formula for the number of n combinations taken r at a time is given by Crn=n!r!n-r!.

Q: There are nine different marbles in a bag. A student reaches in and randomly draws one marble at a…

A: Given there are nine different marbles in a bag. A student reaches in and randomly draws one marble…

Q: The average age of a group of students is 12 years old. There are only 11-year- olds and 14-year…

A:

Q: a) How many three-digit numbers less than 700 can be made using the digits 9, 7, 4, and 2? (Each…

A:

Q: in a physiology class, a student must dissect three different specimens. The student can select one…

A: This question can be solved using the concept of combination.

Q: A pianist plans to play 5 pieces at a recital from her repertoire of 25 pieces. How many different…

A: Solution is given below:

Q: In the United States, telephone numbers consist of a three-digit area code followed by a seven-digit…

A: Given problem Given that   In the United States, telephone numbers consist of a three-digit area…

Q: There are ducks and pigs in a farm. Together, there are 35 heads and 100 legs. Assuming that each…

A: Simplification

Q: A pianist plans to play 4 pieces at a recital from her repertoire of 27 pieces. How many different…

A: Given problem is from selection method of combination where order doesn't matter .  It's formula is…

Q: Charles has eight different winter scarves, and he wears three at a time. How many different ways…

A: Given that       Charles has eight different winter scarves and he wears three at a time  We have to…

Q: Radio stations that are on the east side of a nation have call letters consisting of a W followed by…

A:

Q: A pianist plans to play 5 pieces at a recital from her repertoire of 22 pieces. How many different…

A: Permutation formula: nPr = n!/(n-r)!

Q: In a class of 60 students,each of the students passed either in mathematics or in science or in…

A: Given: Total number of students passed either in mathematics or in science or in both=60 Students…

Q: A time traveler can take 5 books with him, and he has 76 books to choose from. How many different…

A:

Q: In a group of dogs and their owners, there are exactly 20 heads and 64 legs.  How many dogs are in…

A: Let, x be No of men. y be no of dogs   Men consists of 2 legs and dog has 4 legs.   x+y=20 2x+4y=64

Q: Only 30% of teams beat The Great Escape Challenge. If 15 teams beat the challenge, how many teams…

A: It is given that 15 teams beat the challenge, which is the 30% of the teams that played The Great…

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

A:

Q: In a certain class there are a total of 29 majors in mathematics, 21 majors in philosophy, and 7…

A:

Q: A professor gives his students 8 essay questions to prepare for an exam.  Only 5 of the questions…

A: Here, 5 are to selected from 8 options where order does not matter.

Q: In the Americas, automobile license plates contain two letters, followed by four digits. How many…

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

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: At a charity benefit with 33 people in attendance, three $50 gift certificates are given away as…

A:

Q: ianist plans to play 6 pieces at a recital from her repertoire of 26 pieces.  How many different…

A: Total number of pieces available (n) = 26 pieces. Number of pieces (r) which a pianist needs to play…

Q: When five is added to three more than a certain number, the result is 19.What is the number?

A: Let the number be x When five is added to three more than a certain number = 3x + 5

Q: How many children are there in a family wherein each girl has as many brothers as sisters, but each…

A: Let assume Number of sister = x Number of brother = y

Q: The cafeteria is serving french toast, cereal, and fruit. If a student may choose any two of those…

A:

Q: A clerk at a bookstore is restocking a shelf of the best-selling novels. He has two copies each of…

A: Part 1: The total number permutations in which 6 books can be arranged is 6! Since there are three…

Q: a professor gives his students 8 essay questions to prepare for an exam. Only 5 of the question will…

A: the objective is to find how many different exams are possible.

Q: A medical student has to work in a hospital for five days in January.  However, he is not allowed to…

A: there are 31 days in January Out of 31 days , student has to work 5 days therefore the non working…

Q: A pianist plans to play 4 pieces at a recital from her repertoire of 25 pieces. How many different…

A: Given : No. of repertoire pieces = 25 A pianist plans to play 4 pieces i.e n = 4

Q: In a group of students, 100 students know Hindi, 50 know English and 25 know both. Each of the…

A:

Q: In a certain state, all car license plates have four capital letters followed by three digits. How…

A: Given Car license plates have 4 (A to Z) capital letters followed by 3 (0 to 9) digits

Q: A class of 20 students is seated in a classroom with 5 rows of 4 seats each. How many ways are there…

A: Number of ways in which n students can be divided into k groups of h students is given by,

Q: At a lottery, 100 tickets were sold and three prizes are to be given. How many possible outcomes are…

A:

Q: How many ten-digit telephone numbers are possible if the first three digits must all be different?

A: Given,total no.of digits=10  (0 to 9)

Q: If you have six books, but there is room for only four books on the shelf, in how many ways can you…

A: From the given information, n=6 and r=4.

Q: A student needs eight more classes to graduate. If she has met the prerequisites for all the…

A: Given ,A student needs 8 more classes to graduate.

Q: in a row on his bedroom wall, but only has space for 5 of them. If his favourite poster must go in…

A: In how many ways can Liam put the posters up :

Q: A dance club needs 3 new members. If there are 5 males and 9 females applicants, in how many ways…

A: Solution

Q: A time traveler can take 4 books with him, and he has 98 books to choose from. How many different…

A:

Q: A fan of country music plans to make a custom CD with 14 of her 26 favorite songs. How many…

A:

Q: A student is to answer 10 out of 13 questions on an exam. (i) How many if he must answer exactly 3…

A: It is an important part of statistics . It is widely used .

Q: A witness to a hit-and-run accident tells the police that the license plate of the car in the…

A: The first letter has only one(A) chance, the second letter has 26 ways, the third letter has 26…

Q: A pianist plans to play 5 pieces at a recital from her repertoire of 18 pieces. How many different…

A: Given :  A pianist plans to play 5 pieces at a recital from her repertoire of 18 pieces.  Use…

Q: In a certain class there are a total of 37 majors in mathematics, 18 majors in philosophy, and 5…

A:

Q: A pianist plans to play 6 pieces at a recital from her repertoire of 26 pieces. How many different…

A: In this case arrangement matters.  So we will use the permutation method.  He has to pick 6 pieces…

Q: A student needs 9 more classes to graduate. If she has met the prerequisites for all the classes,…

A: The formula for combination is nCr = n! / [r! (n – r)!] = [n (n – 1) … (n – r + 1)]/r!. Explanation:…

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.