A bag contains three red marbles, three green ones, one lavender one, two yellows, and one orange marble.  How many sets of five marbles include at least two red ones?

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

A: At most one of the yellow ones means 0 or 1 yellow ones. There are 3 yellow marbles.  And…

Q: During the fall semester a school is offering science courses in physics, biology, and chemistry,…

A: It is given that there are science courses in physics, biology, and chemistry, and humanities…

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

A:

Q: A restaurant offers 7 choices of main course, 8 sides, 5 appetizers, 7 beverages, and 3 desserts.…

A: Main course  = 7 Sides = 8 Appetizers = 5 Beverages =7 Desserts = 3 We have to find the total number…

Q: A college freshman must take a science course, a computer science course, and a mathematics course.…

A:

Q: .A college freshman must take a science course, a humanities course, and a mathematics course. If…

A: Solution

Q: A bag contains 2 red marbles, 5 green ones, 1 lavender one, 5 yellows, and 3 orange marbles.  How…

A: Since we are making set, so the order will not matter.   If we select the lavender one, then we can…

Q: How many different teams of 4 4 can be chosen from a group of 15 15 children and 17 17 adults if…

A: Given: Number of children = 15 Number of adults = 17

Q: A restaurant offers a menu with 5 appetizers, 5 main dishes, and 4 desserts.  If Zoey is low on cash…

A:

Q: A certain eatery offers a meal that serves a combination of a soup, sandwich and beverage. There are…

A: The given data is: Two kinds of soup (corn or asparagus) 4 sandwiches (chicken, ham, mushroom, or…

Q: A basketball team consist of two centers, five forwards and four guards. In how many ways can the…

A:

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

A: Combination: It means to determine the number of possible arrangements in a collection of items. It…

Q: A restaurant offers 4 different flavours of coffee, 3 different soup selections and 4 different…

A: From the provided information, A restaurant offers 4 different flavours of coffee, 3 different soup…

Q: The Senate in a certain state is comprised of 53 Republicans, 44 ​Democrats, and 33 Independents.…

A: The number of ways to select 33 Republicans is 53C33.The number of ways to select 22 Democrats is…

Q: A buffet has 7 main dishes and 4 desserts. How many different combinations can one choose, if one…

A: Find the number of different combinations can one choose if one takes at least 1 and at most 3 main…

Q: A bag contains 4 red marbles, 3 green ones, 1 lavender one, 3 yellows, and 2 orange marbles. How…

A: Since it is set so order does not matter. we will use combination method At least three means 3 or 4…

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

A: A bag contains  2 Red marbles 2 Green marbles 1 Lavender marble 3 Yellow marbles 4 orange marbles

Q: cafeteria offers a complete dinner that includes one serving each of appetizer, soup, entrée, and…

A: First of all we will list the total different choices we have for each of the things

Q: Colin has 9 cd’s in his carrying case – two John Tesh, three Michael Jackson, and four Beatles. How…

A: Given: Number of cds = 9 Number of John Tesh cds = 2 Number of Michael Jackson = 3 Number of Beatles…

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

A:

Q: In a group of 60 people, 27 like cold drinks and 42 like hot drinks and each person likes at least…

A:

Q: A group of 10 men and 12 women must select a five-person committee. How many committees are possible…

A: a) Since it is a group of people, so order does not matter. We will use the combination for this…

Q: A complete meal is composed of 1 cup of rice, 1 viand, 1 glass of drinks and 1 dessert. If there are…

A:

Q: The United States Senate Committee on Commerce, Science, and Transportation consists of 23 members,…

A: Combinations: The number of combinations of r items selected from n items is, nr=n!n-r!r! Selecting…

Q: A football squad consists of three centers, ten linemen who can play either guard or tackle, three…

A: Given A football squad consists of three centers, ten linemen who can play either guard or tackle,…

Q: 5a. A bag contains two red marbles, six green ones, one lavender one, two yellows, and four orange…

A: These are combination problems.

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

A: There are number of marbles in bag: Number of red marbles: 4 Number of green marbles: 3  Number of…

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

A: Solution: Given information: Red marbles = 3 Green marbles = 3  Lavender  marble = 1 Yellow marble =…

Q: A boy owns 2 pairs of pants, 3 shirts, 8 ties, and 2 jacket. How many different outfits can he wear…

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

A: Solution: From the given information, a bag contains three red marbles, three green ones, one…

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

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

Q: A college offers 2 introductory courses in​ history, 1 in​ science, 1 in​ mathematics, 4 in​…

A: a) In this case, the freshman takes one course in each area during her first semester.

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

A: It is given that there are three red marbles, two green marbles, one lavender marbles, two yellow…

Q: How many breakfast meals consisting of a fruit, a sandwich, and a drink are possible if one can…

A:

Q: a club consists of 5 men and 4 women. in how many ways can this club elect a president, Vice…

A: Given data A club consists of 5 men and 4 women

Q: A menu offers a choice of 5 salads, 15 dishes, and 3 desserts. How many different meals consisting…

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

Q: How many ways can a delegation of 2 Republicans, 2 Democrats, and 2 Independents be selected from a…

A: Given dataRepublicans = 4Democrats = 4Independent = 3

Q: A bag contains 5 red marbles, 2 green ones, 1 lavender one, 2 yellows, and 3 orange marbles.  How…

A: Since we will make sets, so order does not matter. So we will use combination.  Atmost one of the…

Q: In a group of 100 persons, 72 people can speak English and 43 can speak French. How many can speak…

A: In a group of 100 persons, 72 people can speak English and 43 can speak French. How many can speak…

Q: how many teams can be made if they must all be boys?

A:

Q: A group of 13 people consisting of 3 freshmen, 2 sophomores, 4 juniors, and 4 seniors are selected…

A: Given: A group of 13 people is to be formed by selecting, 3 freshmen out of 6 freshmen, 2 sophomores…

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

A: Consider the provided statement of the question,Here given, a bag contains,3 red marbles, 2 green, 1…

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

A: Total number of marbles, n = 3 red + 1 green + 1 lavender + 3 yellow + 3 orange = 11 Number of red…

Q: A company has 7 male and 12 female employees, and needs to nominate 2 men and 2 women for the…

A:

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

A:

Q: There are  10  women and  5  men signed up to join a ballroom dance class. In how many ways can…

A:

Q: How many committees of six can be formed from 18 Republicans and 20 Democrats if three members of…

A: Provided information: Number of Republicans members = 18 Number of Democrats members = 20

Q: A restaurant offers a 4 kinds of soup, 7 kinds of main dish, 5 kinds of vegetable dish, and 6 kinds…

A: A restaurant offers a 4 kinds of soup, 7 kinds of main dish, 5 kinds of vegetable dish, and 6 kinds…

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

A:

Q: In a group of 80 people, 50% of them like Summer season, 70% of them like Winter season. If each…

A: