A total of 50 students are in a class and they are to be divided into groups of 5. How many different combinations of students are possible?

Q: How many six-person volleyball teams be made from a group of six men and three women if: a. If two…

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Q: How many different teams of 44 can be chosen from a group of 1818 children and 1515 adults if each…

A: It is given that the number of children is 18 and the number of adults is 15.

Q: In order to get a bachelors degree in biology, a student at IU needs to take 3 math courses from a…

A: Given: Number of math courses that are to take from a set of 7 courses  = 3 Number of chemistry…

Q: How many combinations can the seven colors of the rainbow be arranged into groups of three colors…

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

A: According to provided data, there is total of 15 children (C) and 17 adults (A). Therefore, the…

Q: Assume that you have a committee of 12 members, made up of 3 men and 9 women. In how many ways can…

A: We have to find given probability..

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: From a group of 7 men and 6 women, five persons are to be selected to form a committee so that at…

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Q: Suppose a class consists of 4 students majoring in Mathematics, 3 students majoring in Islamic…

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Q: Suppose there is a club of 15 people. In how many ways can a committee of 3 people be selected?

A: Our objective is to find the number of way

Q: A store sells 8 kinds of balloons with at least 30 of each kind. How many different combinations of…

A: 8 kinds of balloons with at least 30 of each kind We have to find how many different combinations of…

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: Assume that you have a committee of 11 members, made up of 6 men and 5 women. In how many ways can…

A: Determine the number of ways can the 3 tasks be assigned so that both men and women are given…

Q: A class has 10 boys and 12 girls. In how many ways can a committee of four be selected if the…

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Q: Assume that you have a committee of 15 members, made up of 9 men and 6 women. In how many ways can…

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Q: A group of 11 people consisting of 1 freshmen, 3 sophomores, 3 juniors, and 4 seniors are selected…

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Q: A committee of six people is chosen from eight women and seven men.  How many          different…

A: Solution: From the given information, there are 8 women and 7 men. Here, 6 people are chosen at…

Q: A group of Mathematics faculty at the local college consists of 10 women and 10 men. Five people are…

A: Given  No of men = 10 No of women = 10 We need to select 5 people

Q: A group of 18 people have gotten together to play baseball. They will divide themselves into two…

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Q: A certain committee has organized a retreat for all couples, where the couples are to sit around a…

A: SolutionGiven A certain committee hasorganised a retreat for all couples, wherethe couples are to…

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

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Q: Suppose a class consists of 5 students majoring in Mathematics,5 students majoring in Islamic…

A: The class consists of 5 students majoring in Mathematics,5 students majoring in Islamic Studies and…

Q: Suppose a class consists of 5 students majoring in Computer Science, 5 students majoring in…

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Q: Suppose a class consists of 4 students majoring in Computer Science, 5 students majoring in…

A: The above problem is based on the combinations.     A combination is the selection of items where…

Q: From a group of 8 men and 6 women, six persons are to be selected to form a committee so that at…

A: Given information 8 men and 6 women Six persons are to be selected to form a committee

Q: A club with 5 members is to choose 3​ officers: ​ president, vice-president, and​…

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Q: A particular brand of shirt comes in 12 colors, has a male version and a female version, and comes…

A: Producer Rule: if one event can occur in m ways and a second event can occure in n ways the numbers…

Q: Suppose that there are 9 female and 12 male students in a classroom. How many different 5-member…

A: Combination:   A combination is a selection of objects where order is not important.   If n is…

Q: Suppose a designer has a palette of 14 colors to work with, and wants to design a flag with 4…

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Q: From 6 English teachers and 5 Mathematics teachers, committee of 5 teachers will be organized. How…

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Q: Suppose a class consists of 3 students majoring in Computer Science, 4 students majoring in…

A: Students in computer science CS = 3 Students in mathematics MS= 4 Students in Islamic studies IS= 4

Q: A committee has 10 members and 4 members must be chosen for a subcommittee. Three of the 10 members…

A: Statisticians/mathematicians use different counting techniques while selecting or arranging members…

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

A: Here use combination

Q: How many different teams of 3 can be chosen from a group of 9 adults and 8 children if each team…

A: There are 9 adults and 8 children. A team has to be selected with 3 members.

Q: Suppose a designer has a palette of 16 colors to work with, and wants to design a flag with 2…

A: Recall:  nCr=n!r! (n-r)! We have, n=16, r=2

Q: Suppose a library has at least 6 copies of mathematics book, at least 6 copies of a physics book,…

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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 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: A committee of 5 students are to be chosen from 25 CS majors and 15 Math majors. How many of these…

A: Exactly 3 CS major students can be selected from 25 CS major students in, 25C3 ways, i.e. 2300 ways.…

Q: A group of 11 people consisting of 2 freshmen, 1 sophomores, 4 juniors, and 4 seniors are selected…

A: Given:A group of 11 people consisting of 2 freshmen, 1 sophomores, 4 juniors, and 4 seniors are…

Q: How many committees of 4 can be made from a group of 20 republicans and 15 democrats if at least 1…

A: Since we need at least 1 republican and at least 1 democrat in the committee. So we pick 1 of each…

Q: From a group of 7 men and 6 women, five persons are to be selected to form a committee so that at…

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Q: From a group of 14 newly hired office​ assistants, 5 are selected. Each of these 5 assistants will…

A: Given dataNo of newly hired assistants = 145 to be selected5 assistant can be selected in 14C5…

Q: A committee of 4 people need to be selected from twenty numbers of an organization. How many…

A: Given, A committee of 4 people need to be selected from twenty numbers of an organization.

Q: A five-person committee is to be selected from an organization's membership of 19 people. How many…

A: It is given that, An organization has 19 people out of which 5 person committee is to be selected.…

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: A certain elementary school club has 50 members, 20 of which are girls and 30 are boys. If the club…

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