As the project manager of a project, you are in charge of a team of seven people which includes yourself. You need to form a sub-group within the team that should have four members. How many different groups of four can you form from your seven-person team? Also whether or not you are in the sub-group does not matter. Do you need to use combinations or permutations? Why?

Q: At the end of the day, a bakery gives everything thatis unsold to food banks for the needy. If it…

A: Consider, Number of apple pies left (n) = 12 Number of food banks (r) = 6

Q: A shipment of 50 calculators contains 3 that are defective. In how many ways can an inspector choose…

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Q: How many ways can a delegation of 4 Republicans, 3 Democrats, and 3 Independents be selected from a…

A: Given data Number of Republicans = 9 Number of Democrats = 9 Number of Independent = 4

Q: If 5 cards are dealt from a standard deck of cards, how many different ways can three clubs and two…

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Q: A Zoom class has 48 students, and for an in-class activity they will be going into breakout rooms in…

A: a) The number of different breakout room assignments if the breakout room numbers matters is,…

Q: There are 8 nickels, 5 dimes, 7 quarters, and 6 loonies in a piggy bank. You are thinking of…

A: Given, in a piggy bank, there are  8 nickels, 5 dimes, 7 quarters, and 6 loonies.

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

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Q: In a certain pizzeria you can choose among 3 sizes, 2 crust options, and 5 toppings. If it is…

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Q: Find the number of ways in which we can select a team of 6 players from a class of 12 people.

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Q: How many ways can a delegation of 4 Republicans, 4 Democrats, and 2 Independents be selected from a…

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

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Q: A business has hired 12 new employees and must assign 8 to the day shift and 4 to the night shift.…

A: We have given that  A business has hired 12 new employees and must assign 8 to the day shift and 4…

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: . A shipment of 50 calculators contains 3 that are defective. In how many ways can an inspector…

A: we have to find number  of ways..

Q: If a team of four players must be made from eight boys and six girls, how many teams can be made if…

A: 1. There are eight boys and six girls, totally there are 14 players. A team of four player. The…

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

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Q: in how many ways can a jury of 5 men and 7 women be selected from 10 men and 10 women?

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Q: How many ways can a delegation of 5 Republicans, 5 Democrats, and 2 Independents be selected from a…

A: As we need to choose any 5 republicans from a group of 7 republicans, so we have 7C5 possible ways.

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

A: According to the provided information, number of female students = 9 number of male students = 12…

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

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Q: 24. Box A contains 7 balls and box B contains 16 balls. How many different selections of 10 balls…

A: Determine the different selections of 10 balls that can be made. The different selections of 10…

Q: If 5 cards are dealt from a standard deck of​ cards, how many different ways can three spades and…

A: 5 cards are dealt from a standard deck of​ 52 cards. There are 13 spade cards. Therefore number of…

Q: How many different sets of 6 cards each can be formed from a standard deck of 52 cards?

A: Please find attachment for the details solution

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

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Q: A student committee is to consist of 2 freshmen, 4 sophomores, 3 juniors, and 5 seniors. If 11…

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Q: From 6 female employees and 5 male employees, how many groups of 5 employees can be organized…

A: There are 6 female employees and 5 male employees.

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

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

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Q: In how many ways can a committee of three consisting of two lady engineers and one mal engineer can…

A: Given that  Committee consists of members  = 3  [ Lady engineers = 2 ; Male engineer =1 ] Lady…

Q: If radio station call letters must begin with either K or W and must include either two or three…

A: Multiplication Rule of Counting:If there are p selections for the 1st option, q selection for the…

Q: The number of permutations of n items is also called as _______________.

A: The number of permutations of n items is also called as n! (n Factorial).

Q: How many different sets of 5 cards can be formed from a standard deck of 52 cards?

A: We need to find the number of different 5 card sets that can be formed from a deck of 52 cards. Now,…

Q: In how many ways can a subcommittee of eight be chosen from a Senate committee of seven Democrats…

A: We have to find In how many ways can a subcommittee of eight be chosen from a Senate committee of…

Q: An appliance store carries 9 types of washing machines and 5 types of dryers. A shopper comes in and…

A: Total number of washing machines = 9 Total number of dryers = 5

Q: In how many ways can 5 boys and 4 girls be arranged on a bench if there is no restriction? How about…

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Q: Your club would like to form a committee that has 2 sophomores, 3 juniors, and 4 seniors. If there…

A: In this question out of 7 sophomores we have to choose 2, Out of 8 juniors, we have to choose 3 and…

Q: Your sister is shopping at an exclusive Rodeo Drive clothing store and examines 4 distinct blouses,…

A: It is given that there are 4 distinct blouses, 5 distinct dresses, and 2 distinct handbags. Since,…

Q: From the 9 male and 6 female sales representatives for an insurance company, a team of 2 men and 2…

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

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Q: how many ways can a group of 4 boys be selected from 9 boys?

A: We have to select 4 boys from 9 boys

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 5 married couples, we want to select a group of 3 people. How many choices are there if the…

A: It is an important part of statistics. It is widely used .

Q: From a group of 10 boys and 6 girls a committee of 3 boys and 2 girls is to be selected. In how many…

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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: If you pick 4 cards without replacement from a standard deck of 52 cards, how many different…

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Q: If the chair of a math department has to appoint a committee of 4 professors from among the 10…

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

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

A: