\item How many ways can a store manager arrange a group of 1 team leader and 3 team workers from his 25 employees?

Q: A committee of 6 U.S. senators is to be formed with 3 Democrats and 3 Republicans. In how many ways…

A: We have given that,  Number of Democratic senators = 69 Number of Republican senators = 31

Q: To prepare for a safe grad, a committee of 6 people must be formed from a group of 5 teachers and 6…

A: To determine the number of ways the committee can be formed.

Q: Tony and Maria are two star-crossed lovers trying to get on a committee of 4 people. If there are 10…

A: Consider that the 10 people includes Tony and Maria.

Q: A company has 10 male and 11 female employees, and needs to nominate 3 men and 3 women for the…

A:

Q: In how many ways can 2 pizza toppings be chosen from 12 available toppings?

A: We have given that 2 pizza toppings be chosen from 12 available.

Q: A university hires 7 male instructors and 4 female instructors. In how many ways can it choose from…

A:

Q: How many ways can the top four cash prices be awarded in a lottery that sold 150 tickets if each…

A: here given scenario is with replacement ,

Q: Suppose a department contains 12 men and 15 women. How many ways are there to form a committee with…

A:

Q: A committee of 6 people is chosen from 7 women and 7 men. How many different committees are possible…

A: Since it is a group of persons so the arrangement does not matter.  We will have to use the…

Q: How many ways are there to seat six boys and eight girls in a row of chairs so that no two boys are…

A: See the attachment

Q: There are 20 male and 15 female students in a class. In how many ways can you choose a committee of…

A: Thanks for the question :)And your upvote will be really appreciable ;)

Q: how many ways can a coach choose four players from eight bench players to replace four of the five…

A: The number of ways in which r different items can be chosen from n different items is given as Crn…

Q: A baseball team has 13 members: 10 male and 3 female. How many ways are there for choosing a roster…

A: Given that a baseball team has 13 members: 10 males and 3 females,

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: A developer of a new subdivision wants to build homes that are all different. There are five…

A: Given, no.of interior plans=5no.of exteriors plans=7

Q: How many ways can you select a committee of 4 student our of 10 students?

A: As per our guidelines we are suppose to answer only one question4)Given Total no.of…

Q: A company has 8 male and 7 female employees, and needs to nominate 3 men and 3 women for the company…

A: Number of male employees = 8 Number of female employees = 7

Q: There are 4 purple plates and 4 blue plates? How many different ways can the plates be stacked? Two…

A: see the hand written solution:

Q: If there are 3 representatives from Company A and 4 representatives from Company B meet. If they…

A: This is a application of Fundamental Principle of Counting .

Q: There are 13 female board members and 17 male board members. How many ways are there to make a…

A: Given there are 13 female board members and 17 male board members. To find number of ways are there…

Q: There are 9 female board members and 21 male board members. How many ways are there to make a…

A: We use combination to find number of way to make a committee.

Q: The number of ways to distribute 9 toys to 4 children so that the youngest child receives 3 toys and…

A:

Q: The math club needs to send 4 representatives – 2 females and 2 males to a meeting. If there are 12…

A: GivenNo. of female math club members = 12No.of male math  club memebrs = 23no.of representatives  to…

Q: Tony and Maria are two star-crossed lovers trying to get on a committee of 3 people. If there are 10…

A: In the question,Tony and Maria are trying to get on a committee of 3 people,Total number of eligible…

Q: The senate in a certain state is comprised of 59 Republicans, 38 Democrats, and 3 Inpendents. How…

A: Given that the senate in a certain state is comprised of 59 Republicans, 38 Democrats, and 3…

Q: Determine the number of ways such that 5 men and 5 women be seated at a round table if no two women…

A: No. of men = 5  No. of women = 5

Q: How many Ways can 5 Pants, 5 Shirts and 2 Belt combination can be worn?

A: How many Ways can 5 Pants, 5 Shirts and 2 Belt combination can be worn?

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: A grocery pick-up service has 12 appointment openings one morning. If 8 customers have signed up…

A: Combinations: It defines the number of possible ways an object can be selected from a group. In…

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: How many formations of committee from 10 persons are possible if the committee consists of one…

A: In this question, the concept of Permutation and Combination is applied. Permutation  Permutations…

Q: A computer company has 5 vaccines in its executive trainee program. The company must select the…

A: Given - A computer company has 5 vaccines in its executive trainee program. The company must select…

Q: Find the number of ways in which 5 economics books, 3 history books, and 2 mathematics books can be…

A: See the detailed solution below.

Q: Find the number of ways that 6 teachers can be assigned to 4 sections of an introductory psychology…

A: It is given that, 6 teachers can be assigned to 4 sections. We have to find the no. of ways that 6…

Q: How many ways can Carlos choose 2 pizza toppings from a menu of 20 toppings if each topping can only…

A: The number of pizza toppings chosen is 2 and the total number of toppings is 20.

Q: How many baseball teams of 9 members can be formed from 14 players?

A:

Q: How many ways can 7 people fall in line if 2 persons doesn’t want to be seated next to each other?

A:

Q: A committee of 6 students has to be formed from 10 boys and 8 girls. In how

A: As per Bartleby's guidelines, three parts of the given question can be solved at a given time. Given…

Q: A committee of 4 people is chosen from 8 women and 8 men. How many different committees are possible…

A: Combination: The number of different selections of ‘r’ elements (order doesn’t matter) from a set of…

Q: There are 7 boys and 3 girls in a class. How many different ways can the classroom teacher create a…

A: From the given information,   Number of boys = 7 Number of girls = 3   Total = 10

Q: Tony and Maria are two star-crossed lovers trying to get on a committee of 3 people. If there are 9…

A:

Q: A committee of 6 U.S. senators is to be formed with 3 Democrats and 3 Republicans. In how many ways…

A: Combination Rule:A combination is a selection of all or part of a set of objects, without regard to…

Q: A committee of 6 U.S. senators is to be formed with 3 Democrats and 3 Republicans. In how many ways…

A: Given: There are 33 Democratic senators and 67 Republican senators. Find the number of ways in which…

Q: How may different committees of 3 students( 2 male and 1 female) can be formed from a group of 6…

A: We have to find no of different committee..

Q: How many ways are there to distribute 6 different books among 13 children if no child gets more than…

A: Given: 6 different  are to be distributed among 13 children so that no child gets more than 1 book

Q: A committee of 6 people is chosen from 8 women and 8 men. How many different committees are possible…

A: Given that, a committee of 6 people is chosen from 8 women and 8 men. This is a combination problem…

Q: What are 2 ways to obtain 1 jug with exactly 4 units of water?

A: Given: There are three jugs. 5 unit jug, 3 unit jug, and an emply jug. To determine: 2 ways to…

Q: A teacher will randomly award three students with extra credit. How many possible ways can the…

A: Given that  , a teacher will randomly award three students with extra credit .  Teacher can pick…

Q: How many ways can 6 joggers line up single-file to get a drink from a water fountain?

A: Factorial Rule: The total number of ways n different objects can be arranged where order of the…

Angles in Circles

Angles within a circle are feasible to create with the help of different properties of the circle such as radii, tangents, and chords. The radius is the distance from the center of the circle to the circumference of the circle. A tangent is a line made perpendicular to the radius through its endpoint placed on the circle as well as the line drawn at right angles to a tangent across the point of contact when the circle passes through the center of the circle. The chord is a line segment with its endpoints on the circle. A secant line or secant is the infinite extension of the chord.

Arcs in Circles

A circular arc is the arc of a circle formed by two distinct points. It is a section or segment of the circumference of a circle. A straight line passing through the center connecting the two distinct ends of the arc is termed a semi-circular arc.