A marching band consists of 11 pipers and 12 drummers.  Three of them are selected to march in order in a scaled-down socially-distanced New Year parade.  How many different possibilities are there if the selected trio must include at least one piper?

Q: 1)Tom has 2021 balloons to be evenly distributed among 21 students. If every student receives the…

A: Tom has 2021 balloons .We have distributed in 21 students every students receive balloons…

Q: In a cohort of 46 graduating students, there are 5 different prizes to be awarded. If no student can…

A: A Permutation is the choice of r things from a set of n things without replacement and where the…

Q: If 10 people are qualified for the next flight of a new space vehicle , how many different groups of…

A: Number of different ways to choose r number of people from a given set of n people is given by…

Q: From a pool of 300 candidates the office of president, Vice President, secretary, and treasurer will…

A: Given that,Total number of candidates = 300Total number of required candidates = 4

Q: If a dealer randomly picks 5 cards from a standard deck that consists of 52 playing cards and then…

A: From the above data We are given that Total number of cards = n =52 No of selected cards = r =3

Q: Six people are about to enter a cave in a single row. In how many ways could the arrange themselves…

A: Given: Six people are about to enter a cave in a single row

Q: From a club of 17 people, in how many ways can a group of six members be selected to attend a…

A:

Q: 9 freshmen, 9 sophomores, 8 juniors, and 7 seniors are eligible to be on a committee. In how many…

A: Solve

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: The football team consists of 15 members. In how many ways can a playing team of 11 players be…

A: = 1365Hence, there are 1365 ways to form a football team with 11 players from 15 players.

Q: Suppose a certain combination lock requires three selections of numbers, each from 1 through 25 (b)…

A:

Q: Out of the 12 people applying for a scholarship, a) how many ways can we select a group of five to…

A: N : number of students = 12 a) To select 5 people. = (12),(11),(10),(9),(8)  are the choices for…

Q: Out of 9 children, in how many ways can a family have at least 1 girl?

A: We have given that, 9 children i.e. n=9 and family have at least 1 girl i.e. r=1   Combination…

Q: Assuming that no one can hold more than one office, how many selections are possible?

A: select a president, vice-president, secretary, and treasurer out of a club with 15 members.  Here…

Q: group of 9 grade 11’s and 13 grade 12’s apply to go to a student conference in Vancouver, but there…

A:

Q: If you can choose one item from a group of M items and a second item from a group of N items, then…

A: we have chose 1 item from a group of M items  and second item from a group of N items

Q: A committee of size 6 is being formed from a group of 10 Republicans, 8 Democrats and 4…

A:

Q: How many different eleven-member football teams can be formed from a possible 35 players if…

A: Total no. of possible players = 35 No. of players in a team=11

Q: f there are eleven​multiple-choice questions on an​ exam, each having three possible​ answers, how…

A: Given that  Number of multiple choice questions in exam (n) = 11  Each question has 3 possible…

Q: In a shipment of  59 vials, only 14 do not have hairline cracks. If you randomly select 2 vials from…

A: Given that  Number of vials (n) = 59 Vials do not have hairline cracks = 14 Vials having hairline…

Q: The pool of students in a calculus class consist of 22 sophomore and 8 freshmen. If seven students…

A: (a) Determine the number of different groups of seven students can be selected. The number of…

Q: In a cohort of 25 graduating students, there are 3 different prizes to be awarded. If no student can…

A:

Q: In a certain beauty pageant, there are 10 equally beautiful and talented candidates. In how many…

A:

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: A committee of 8 people randomly chooses 3 people in order to be president, vice president, and…

A: Total person = 8 to chosen = 3 Order = considered

Q: There are 10 people to be selected from. How many committees are possible?

A: Here use combination

Q: From a group of 4 men and 5 women, how many committees of size 3 are possible a) With no…

A: Note: Hi, thank you for the question. As per our company guideline we are supposed to answer only…

Q: a restauranr offers 4 different flavors of coffee,3 different soup selections and 4 different…

A:

Q: How many ways to choose 4 out of the 10 candidates to be sent to a conference?

A: Combination Rule: The arrangement of r objects from n different objects is given by:

Q: In a shipment of  62 vials, only 14 do not have hairline cracks. If you randomly select 3 vials from…

A: The number of vials is 62. The number of vials selected randomly is 3.

Q: (b) From a collection of 52 store customers, 3 are to be chosen to receive a special gift. How many…

A: a group of 52 store customers. 3 persons are to be selected, need to find total way exactly 3 store…

Q: an automobile that was tested for production defects, but assume that the number of production…

A:

Q: A track race has 6 participants. In how many orders could the runners possibly finish

A:

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

A:

Q: How many different selections of three books can be made from a set of fifteen books?

A: Introduction:According to the permutation rule, if r distinct items are to be chosen from n items…

Q: In a group of 6 boys and 4 girls, 4 children are to be selected. In how many ways can they be…

A: The number of ways in which r different items can be selected from n different items, can be given…

Q: Find the number of ways of selecting exactly one of the two best applicants in a selection of two…

A: Given problem Given that

Q: Suppose that a drama class has 22 students. a. In how many ways can four students be selected to…

A: a) We will select a group of 4 students from 22 students. So arrangement is not required. That means…

Q: In a group of 4 people, is it possible for each person to have exactly 3 friends? Why?

A: Let G be a graph with 4 vertices, one vertex representing each person in the group. Join two…

Q: A man has eight shirts and five ties. Assuming that they all match, how many different shirt-and-tie…

A: Given,            A man has eight shirts and five ties.

Q: In a quiz that has ten multiple choice questions, each with three possible choices- What is the…

A: Given information No of questions = 10 Each has 3 possible responses For 10 questions, there are 3 x…

Q: Out of a population of 52 people, how many possible samples of size 2 are there?

A: Given information- Population size, n = 52 Sample size = 2 We have to find the number of possible…

Q: How many different letter arrangements can be made from the letters in the word of ASSASSINATION

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

Q: In a group of 10 boys and 15 girls how many selections of 6 students are possible?

A: There are 10 boys and 15 girls The total number of students is 25 The total number of ways of…

Q: Find the number of full houses in a poker hand, that is, the number of poker hands with three of a…

A: Let there be 4C3 =4 by choosing the 3 cards of the same typesand 4C3 =6  by choosing…

Q: A teacher and his eleven students are standing in a single file line waiting to enter the cafeteria…

A: We have given that a teacher and his eleven students are standing in a single file line waiting to…

Q: A bag contains pieces of 6 different types of candy. If the bag has 85 pieces in total, how many…

A: Explanation:Here givens the 85 prices 6 types of different candys and finally how much randomly…

Q: After selecting nine players for a baseball game, the manager of the team arranges the batting order…

A: Given, After selecting nine players for a baseball game, the manager of the team arranges the…

Q: From a group of 10 men and 12 women, only 5 will randomly sit down in a row of 5 chairs. How many…

A: Solution :-

Q: From a group of 17 smokers and 23 ​nonsmokers a researcher wants to randomly select 6 smokers…

A: We have to find no. Of ways to select people.