In a group of 24 people who like rock, country, and classical music, 14 like rock, 17 like classical, 11 like both rock and country, 9 like rock and classical, 13 like country and classical, and 8 like rock, country, and classical. How many like country?

Q: A committee has 20 people.  In how many ways can a President, Vice-President, and Secretary be…

A: Note:  Permutation: We kno that, nPr represents the selection an ordered set of ‘r’ objects from a…

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 bag contains five red marbles, two green ones, one lavender one, two yellows, and four orange…

A: We first find the number of sets of 5 that includes no green marbles. There are total (5+2+1+2+4)=14…

Q: 2. You have read 175 novels of the 350 in your home, but your sister has read 190, of which only 55…

A: Let us denote : A= number of novels read by me B= number of novels read by sister Given that…

Q: There are 55 runners in a race. How many ways can the runners finish first, second, and third? There…

A: given data number of runners = 55 we have to find no. of ways to finish first ,second and third…

Q: In how many ways could a committee be formed that included 3 Conservatives, 3 Liberals, 2 NDP and 1…

A: Number of conservatives = 14 Number of Liberals = 23 Number of NDP = 8 Number of independent members…

Q: A catering service offers 12 appetizers, 10 main courses, and 9 desserts. A customer is to select 3…

A: 12 appetizers 10 main courses 9 desserts   A customer is to select 3 appetizers, 6 main courses, and…

Q: A computer package comes with two different choices of printer, four different monitors, and 3…

A: Multiplication rule of counting: If there are ‘a’ number ways to make the first choice, b ways to…

Q: A bag contains four red marbles, three green ones, one lavender one, three yellows, and one orange…

A:

Q: How many ways can a jury of 5 women and 6 men be selected from 13 women and 12 men

A:

Q: Baseball teams have an active roster of 25 players, but only 9 players play in the field at once. Of…

A: The given data is as follows:The objective is to compute the number of ways in which one can choose…

Q: In how many ways can a committee of three men and two women from eight men and six women

A: given data  make committee of 3 men and 2 womens from 8 mens and 6 womens.

Q: A company has 42 employees. How many different ways can 7 people be chosen to serve on a committee…

A: We can choose the 7 persons in 42C7 ways  Where 7 people are chosen then there are (42-7)=35 people…

Q: A merchant surveyed 380 people to determine the way they learned about an upcoming sale. The survey…

A:

Q: There are 42 runners in a race. How many ways can the runners finish first, second, and third? There…

A: there are 42 runners in a rece we have to find out the no. of ways can finish first, second and…

Q: in how many ways can a jury of 5 men and 7 women be selected from 10 men and 10 women?

A:

Q: How many ways can a delegation of 55 Republicans, 55 Democrats, and 22 Independents be selected from…

A: Given data Number of Republicans = 77 Number of Democrats = 77 Number of Independent = 33

Q: A card deck consists of 9 fire Pokemons and 11 ice Pokemons. How many ways can 7 cards be chosen…

A: The objective of the question is to find the number of ways to choose 7 cards from a deck of 20…

Q: In a certain class, 20 students do not like Spider-Man nor Dark Knight. In the same class, 74…

A:

Q: Assume that there are 105 students: 45 of which like rock, 52 of which like country, and 23 of which…

A:

Q: At a certain university 523 of the seniors are history majors or math majors (or both). There are…

A:

Q: A test consists of 12 questions that are divided into three questions. There are 5 questions in the…

A: Given: Questions in first section =3 Questions in second section =2 Question in third section =1

Q: A group of 100 people touring Europe includes 38 people who speak spanish, 58 who speak portuguese,…

A:

Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.