78. Choosing a Group Sixteen boys and nine girls go on a camping trip. In how many ways can a group of six be selected to gather firewood, given the following conditions? (a) The group consists of two girls and four boys. (b) The group contains at least two girls.

Q: 3) Suppose the math club as 14 members. How many ways can they select a president, a vice president,…

A: Combination is used when the problem is related to selection only and the sequence of selection or…

Q: a) You are thinking of buying a car which has 6 different engine types, 8 different interior types,…

A: Given information 6 different engine  8 different interior type 13 different colour schemes a) No of…

Q: 3. You have a bag of 100 marbles, and it contains 6 different types of marbles. You decide you want…

A:

Q: 3. a) How many ways are there to select three math help websites from a list that contains six…

A: Given that: a. 3 math help websites from 6 different sitesb. 3 cars and 4 trucks from 8 cars and 11…

Q: a. A coin is tossed 3 times. Find out the number of outcomes. b. In how many ways can the letters of…

A: a) When tossed a coin 3 times then  then we have possible combinations of outcomes  are - { HHH,…

Q: eight students from a pool of nine female students and seven male students are to be selected to…

A: Given, There are nine female students and seven male students. We want to select eight students.

Q: License Plate You want your lieeuse plate to consist of 3 letters grouped together and 3 digits…

A: Given: 3 letters and 3 digits

Q: 15. Arun wants to send invitation letter to his 7 friends. In how many ways can he send the…

A: There are 7 friends and 4 servants.We can see that each of 4 servantscan invite each of 7 friends,…

Q: 15. In how many ways can the 8 members of the committee be chosen from 15 senior and 10 junior…

A: Here use combination

Q: b) A catering service offers 7 appetizers, 9 main courses, and 8 desserts. A banquet committee…

A: Given : 7 appetizers, 9 main courses, and 8 desserts.

Q: 6 A committee of 6 officials is to be chosen from 8 men and 7 women. If the committee is to maintain…

A: Committee selections , using permutations and combinations

Q: A person is playing a card game in which they receive 3 cards from a dealer. If the order doesn't…

A: The answer is given as follows :

Q: 1. a) An employer must hire 2 people from a list of 13 applicants. In how many ways can the employer…

A: 1. a) so employer have to hire 2 people from a list of  13 applicants, Here we use nCr = n!r!(n-r)!…

Q: 18. A woman has 10 close friends. Find the number of ways in which she can invite 4 of them to…

A: Given data: The total numbers of friends are n=10. The numbers of friend invite to dinner are r=4.…

Q: 10. A total of 55 pupils are required to choose between two activities during school holidays. 28…

A:

Q: 16. The debate club has 18 members, but only 4 can compete at the next meet? How many 4-person teams…

A: 16) Given Information: There are 18 members in the debate club. Only 4 can compete in the next meet.…

Q: 2. Suppose you bought a lot from a shopping spree. You have 3 new shirts, 4 new jeans, 4 different…

A: The number of ways to select r number of different objects, from n number of different objects, can…

Q: 1) A basketball team contains 20 players. If 5 people can be on the court at one time, how many…

A:

Q: 10. There are 11 women and 9 men in the math department. (a) How many ways can a committee of 4…

A: The combination rule of counting is used when the order of selection does not matter. So the number…

Q: 6. The University of Montana ski team has 15 entrants in a men's downhill ski event. The coach would…

A: 6) The number of entrants in men’s downhill ski event is 15.

Q: 5) You have been asked to judge an art contest with 15 entries. In how many ways can you assign 1st…

A:

Q: 12 players for a softball team show up for a game: (a) How many ways are there to choose 10 players…

A: a) We can pick a group of 10 players from 12 players in 12C10=66 ways.

Q: 3. There are six men and five women in a room. We are going to choose five people from the room. a)…

A: Disclaimer: Since you have asked multiple questions, we will solve the first question for you. If…

Q: 5. An electronic company employed 6 sales representatives and 9 product designers this year in a…

A: We have to find given all no of ways...

Q: A company that makes crayons is trying to decide which  5  colors to include in a promotional…

A: In this question a company that makes crayons is trying to decide which 5 color to include in…

Q: 7) A tourist in France wants to visit 12 different cities. How many different routes are possible?…

A: Answer of q-7    12 different city to visit We have to find nom of different routes possible Here…

Q: A box contains 11 red marbles, 7 green marbles, and 6 black marbles. A sample of 10 marbles is to be…

A: Hello! As you have posted 4 sub parts, we are answering the first 3 sub-parts.  In case you require…

Q: Ten students in a Mathematics contest are competing for first, second and third prize. How many ways…

A:

Q: 6. In the Camarillo Air Race eight planes are entered and there are no ties, in how many ways can…

A: We will use the simple layman approach to the problem.

Q: 28. A box contains 5 green, 7 yellow, and 10 orange ping pong balls. How many ways can 5 balls be…

A: As per our guidelines we are suppose to answer three sub parts. Given,no.of green balls=5no.of…

Q: 20 persons are sitting around a table. How many ways can we choose 3 persons, no two of whom are…

A: Obtain the number of ways of choosing 3 persons, no two of whom are neighbors. The number of ways of…

Q: Andy, Bandy, Candy, Dandy, Endy and Fandy wanted to form a school club. They have decided that there…

A: 2. there are 6 members in total Andy, Bandy, Candy, Dandy, Endy and Fandy we need to select one…

Q: 3. In a gathering, the host makes sure that each guest shakes hands with everyone else. If there are…

A:

Q: 7. A regional committee has 5 members from Town A, 3 members from Town B, and 2 members from Town C.…

A: HERE AS PER GUIDELINES I HAVE CALCULATED 1ST MAIN QUESTION  here use combination

Q: (a) There are 16 appetizers available at a restaurant. From these, Jose is to choose 13 for his…

A: Note: Hi there! Thank you for posting the question. As there are several independent questions,…

Q: 14 players for a softball team show up for a game: (a) How many ways are there to choose 10 players…

A:

Q: 3. You are the owner of World of Woolcraft, a small business with 5 employees that produces custom…

A: This is a problem based on combinations of numbers. Given,  5 employees are there and we need to…

Q: 6. 20 students from American River College and 12 students from Woodland College attend a new…

A: Given data: 20 = students form American River College 12 = students from woodland College 8 =…

Q: 8) There are 11 players on the Dragons basketball team. How many ways can the coach select a group…

A: “Since you have asked multiple questions, we will solve the first question for you. If you want…

Q: 8) In a track meet, ten runners compete for first, second, and third place. How many different ways…

A: Correct answer is =  3! * 103 = 6 * 10*9*83*2*1 = 720

Q: How many ways are there to choose a dozen donuts from 18 varieties: a) if there are no…

A: For the solution follow the next steps

Q: Ten members of a wedding party are lining up in a row for a photograph. (a) How many ways are there…

A: (a) Compute the number of ways to line up ten people as follows. It is known that the number of ways…

Q: In a survey, a group of students is asked their favorite sport. Eighteen students choose “other”…

A:

Q: 2. A bag contains 6 red balls and 4 white balls. In how many ways can one draw: a) 2 white balls b)…

A: As per given by the question, A bag contains 6 red balls and 4 white balls. Now, (a). In how many…

Q: In how many ways can 9 member of the family be seated in a round table with 7 chairs?

A:

Q: 6. Seven cross country runners will be chosen from the SFSU cross country team of 14 to represent…

A: From the given information. The number of cross country runners are 7. Total number of members in…

Q: Suppose that every person in a 26-member student organization is either a first- year, second-year…

A: Given that: Number of students in the organization = 26 Number of categories = 3

Q: 2. A teacher is decorating their classroom by placing posters in a row on one wall. The teacher has…

A: Yes, we will need the Fundamental Counting Principle. Since you figured out the first way, so I am…

Q: 7. What is the number of ways of choosing 4 cards from a deck of 52 playing cards? In how many of…

A: The deck of 52 playing cards is broadly classified into 2 which are further divided into 2…

Q: (7) A. How many ways can 7 people line up in a cafeteria line? B. How many ways can five people be…

A: