A legislative committee consists of 5 Democrats and 6 Republicans. A delegation of 3 is to be selected to visit a small island republic. Complete parts (a) through (d) below. (a) How many different delegations are possible? The 3 delegates can be selected 165 different ways. (b) How many delegations would have all Democrats? The 3 delegates can be selected different ways if all 3 are Democrats.

Q: if there are no restrictions? if Holly and Sam cannot sit together?

A: here given ,  Holly, Parker, Jace, Ola, Amir and Sam have gone out to a football game together, They…

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: In a class there are 30 female students and 20 male students. A committee of four students need to…

A: There are 30 female and 20 male students.

Q: You would like to "build-your-own-burger" at a fast-food restaurant. There are five different…

A: Given : Types of Bread = 5 Types of cheese = 7 Types of cold toppings = 4 Types of sauces = 5

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

A:

Q: A group has 10 men and 7 women. If 6 people are selected for a committee so that the majority of the…

A: Total number of people are 10+7=17 For the committee to be made with majority women, number of…

Q: A senate committee has 15 members.  If a subcommittee of 6 senators is to be formed from the…

A:

Q: A group of nine women and six men must select a four-person committee. How many committees are…

A:

Q: Apolice department in a small city consists of 10 officers. If the department policy is to have 5 of…

A:

Q: At a dinner party, 6 men and 6 women sit in a round table. In how many ways can they sit if Bob,…

A: Number of ways to arrange N person around the round table is (N-1)!. Here, there are 6 men and 6…

Q: A take-out restaurant offers 6 different kinds of sushi. If they have exactly 4 pieces of eachkind…

A: Given: There are 6 different kinds of sushi, with exacctly 4 pieces of eachkind. To determine:…

Q: 2. Dylan, Andrew, Hailey, and Jordan ran in a race of 25 people. In how many different orders can…

A:

Q: 2. In your drawer, there are 4 identical pairs of brown socks and 8 identical pairs of green socks.…

A:

Q: From the 10 male and 12 female sales representatives for an insurance company, a team of 4 men and 2…

A:

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

A:

Q: At a local restaurant, a dinner special consists of choosing a salad, an entree and a dessert. If…

A: If there are 3 choices for salad, 6 choices for the entree, and 4 choices for dessert. At a local…

Q: How many different committees can be formed from 11 teachers and 42 students if In how many ways can…

A:

Q: 5. Rowena would like to invite 7 friends to go on a trip but has room for only 4 of them. In how…

A: Combination:   It is nothing but the selection of objects where the order of selection is not…

Q: Suppose we want to choose 2 letters, without replacement, from the 4  letters A, B, C, and D. How…

A:

Q: The 50 members of a club include both the club president and the club treasurer. All 50 members want…

A: Topic- permutations and  combinations

Q: How many different committees can be formed from 7 teachers and 49 students if the committee…

A: From the provided information, There are 7 teachers and 49 students and the committee consists of 2…

Q: How many ways are there to make a committee of 19 board members if exactly 5 must be female?

A: Given Data: The number of female board members is: f=11 The number of male board members is: m=19…

Q: The board of directors of a corporation must select a president, a secretary, and a treasurer. In…

A: Given that there are total 14 members.    A president, a secretary, and a treasurer represent 3…

Q: From the 10 male and 7 female sales representatives for an insurance company, a team of 4 men and 2…

A: Given that from the 10 male and 7 female sales representatives for an insurance company a team of 4…

Q: Before a trial, a jury had to be selected from a group of 12 males and 13 females. a. In how many…

A:

Q: To fill a number of vacancies, the personnel manager of a company has to choose three secretaries…

A: The number of ways a company has to choose three secretaries from among ten applicants can be done…

Q: In how many ways can the committee of 7 members be selected? How many different committees can be…

A:

Q: A legislative committee consists of 4 Democrats and 7 Republicans, A dolegation of 4 is to be…

A: A legislative committee consists of 4 democrats and 7 Republicans. => Total = 7+4 = 11 A…

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: If a club consist of 15 members, how many different ways are there for the club to fill the…

A: The number of members is 15. The number of position is 3.

Q: Delegates from 10 countries, including Russia, France, England, and the United States, are to be…

A: Given  10 countries in total  4 of them are Russia, France, England, United States  We need to…

Q: A president, a treasurer, and a secretary are to be chosen from a committee with 30 members. In how…

A:

Q: A group of 12 service dogs have been trained as K-9 units to assist the SWAT unit. How many ways are…

A: This is a combinatorics problem. So number of ways to select 3 dogs from 12 is:  C12,3=12!3!12-3!…

Q: How many ways are there to stack an ice-cream cone with 4 scoops if the choices are a. cookie dough,…

A: To calculate the total number of ways to take an ice-cream cone with 4 scoops if the choices are…

Q: 10) If a man can select one of 4 shirts, one of 3 pairs of trousers and one of 2 pairs of shoes, how…

A:

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

A: Total number of players is 20. The number of player to be court at one time is 5.

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: Four married couples have reserved eight seats in a row at the   theater, starting at an aisle seat.…

A: As given above there are four married couples have reserved eight seats in a row. The arrangement of…

Q: For a Halloween party, each guest can choose from the 6 different kinds of candy to have in a prize…

A: Given,no.of different kinds of candy=8

Q: A class of 15 students needs to elect a class president, vice president, treasurer, and secretary.…

A: Consider the given information. The class have 15 student and there are four position as given in…

Q: A president, a treasurer, and a secretary are to be chosen from a committee with 44 members. In how…

A:

Q: How many different committees can be formed from 11 teachers and 48 students if the committee…

A: a) answer = (11C3)*(48C2) = 165*1128 = 186120 Therefore, 186120 committees can be possible with 3…

Q: How many different committees can be formed from 6 teachers and 46 students if the committee…

A: Given information- We have given that we have to form a committee of 5 teachers from 6 teachers and…

Q: A philanthropist, on his free day, seeks to visit an orphanage from the seven orphanages he supports…

A: Given information No of orphanages = 7 No of elementary school = 10 No of care homes = 8

Q: How many ways are there to select 2 people from a group of 7 to serve on a committee? What kind of…

A: We have given there is group of 7 and we have to select 2 people from this group to serve on a…

Q: Two freshmen and three sophomores from a sorority will attend a conference. If the sorority has 12…

A:

Q: How many different committees can be formed from 9 teachers and 32 students if the committee…

A:

Q: If there are five different toy cars, and you want to put fifteen toy cars on the display, how many…

A: Permutation is the measurement of principle counting. It is measure that arrange the data in an…

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