3. There are 5 doors in a Lecture Hall. In how many ways a student can enter the room through one door and leave through another? What if he is also allowed to leave through the door that he has entered?

Q: 6. A University building has 9 doors. In how many ways can a student enter and leave by different…

A: Total no of doors in university = 9 We have to find the no. If ways a student can enter and leave by…

Q: 1/5 of a class study english and 3/5 study math. If the class consists of 80 students, how many…

A: In this question we need to find out how many students study English and math in the class. total…

Q: In how many ways can a team of 11 players be chosen from 14 players if the captain and his assistant…

A: This is problem of counting and we will solve this using combination.

Q: How many ways can we assign 124 students to 4 sections in such a way that Section 1 must have at…

A: Given: There are 124 students and 4 sections Section 1 must have at least 30 students, section 2…

Q: Suppose there are 6 roads connecting town B to town C and 4 roads connecting town C to town D. In…

A: According to the given information in this question  Here are 6 roads connecting town B to C  And 4…

Q: 2. Five boys and four girls are waiting for the MRT to arrive at Guadalupe Station. In how many ways…

A: Hi! Thank you for the question, As per the honor code, we are allowed to answer three sub-parts at a…

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

A:

Q: In how many ways: a. Can 8 people be lined up to get on a bus? b. Can they be seated if 4 specific…

A: Total persons  = 8 people a) There are 8 people, there will be 8 places to arrange (here order will…

Q: 9. There are 5 different roads from City A to City B and 3 different roads from City B to City C. In…

A:

Q: A class consists of 60 girls and 40 boys. In how many ways can a president, vice-president,…

A: Number of boys=40 Number of girls=60 Given the treasurer must be a girl. Hence the number of ways to…

Q: A clothing store has 13 shirts in 4 sizes: small, medium, large, and extra-large for sale. If it has…

A: Number of ways of selling two small shirts is 2! = 2 Number of ways of selling three medium shirts…

Q: how many ways can those offices be​ filled?

A: Given that: A club has 7 members.

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

A: Permutation:   It is nothing but  an arrangement of objects with the definite order.   Let n is the…

Q: 11. In how many ways can 4 boys and 5 girls sit in a row if the boys and girls must alternate?

A: Disclaimer: Since you have asked multiple questions, we will solve the first question (i.e. #11) for…

Q: A woman has nine close friends. (a) In how many ways can she invite six of these to dinner? (b)…

A: Fundamental principle of counting : If an event occur in m ways an corresponding to it another event…

Q: In one state, each automobile license plate shows three letters followed by two digits, or two…

A: The number of letters in alphabet is 26. The number of digits from 0 to 9 is 10.

Q: In how many ways can six men and five women be arranged in a row if no two women is standing next to…

A: Given,no.of mens=6no.of womens=5total no.of peoples=11

Q: A camp counselor and four campers are to be seated along a picnic bench. And how many ways can this…

A: given, A camp counselor and four campers are to be seated along a picnic bench. No of ways of…

Q: 2. In how many different ways can they arrange to give everybody a chance to experience the ride?

A: Number of people=7, number of bike available=4. To find the number of ways of arrangements so that…

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

A:

Q: In how many ways a team of 4 representatives can be chosen in a class of 12 students consisting of 5…

A:

Q: In how many ways can 3 student, 4 teachers and 4 workers sit in a line if the teachers always set…

A:

Q: A camp counselor and six campers are to be seated along a picnic bench. In how many ways can this be…

A:

Q: In how many different ways can the director of a design and structural department choose 2 Civil…

A: Given: Number of applicants to be chosen from 7 applicants are 2. Number of applicants to be chosen…

Q: A woman has 11 close friends. In how many ways can she invite 5 of them to dinner if two of them are…

A: Given, A woman has 11 close friends. To find,  How many ways can she invite 5 of them to dinner if…

Q: There are 10 students in a class. In how many ways can an instructor give at least one student a…

A: There are 10 students So sample size, n= 10 And we've to find ways for at least 1 student. So r= 1

Q: Suppose you have 11 books and you randomly pick 4 to take on vacation with you. How many ways can…

A:

Q: Suppose 12% of students chose to study French their freshman year, and that meant there were 21 such…

A: Given: Suppose 12% of students chose to study French their freshman year and  that meant there were…

Q: A committee of 5 is to be chosen from a group of 10 people. How many ways can it be chosen, if Bill…

A: Below the solution

Q: 4. In how many ways can 5 starting positions on a basketball team be filled with 8 men who can play…

A: The number of men who can play any of the positions is, n = 8 The number of starting positions on a…

Q: Suppose there are 6 roads connecting town A to town B and 4 roads connecting town B to town C. In…

A: Multiplication rule of counting: If there are ‘a’ number ways to make the first choice, b ways to…

Q: In how many ways can 7 women and 7 men partner up for ballroom dancing, if each person has to dance…

A: The number of ways to select r objects from n objects is computed by using the formula of…

Q: 1. The IE Falcons plays 14 games during the COE Basketball Tournament. In how many ways can the team…

A: Note- As per our policy we can answer only 1st question. If you want solutions for other, then you…

Q: 2. A carton of 12 rechargeable batteries contains one that is defective. In how many ways can an…

A:

Q: 10. If there are 15 people and only 2 chairs are available, in how many ways can they be seated?

A: Explanation: Given that,  Number of people=15 Available chairs=2     Formula Used: Crn=n!r!·(n-r)!

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: A club with eleven members is to choose three​ officers: ​ president, vice-president, and​…

A: A club with eleven members is to choose three​ officers: ​ president, vice-president, and​…

Q: 2. In how many ways can six students be seated in a row of six seats if two of the students insist…

A: We have to arrange 6 students on 6 chairs in a row out of which 2 particular students sits beside…

Q: In a manufacturing operation, a part is produced by machining, polishing, and painting. If there are…

A: As per guidelines expert gave to answer first question only

Q: 26. A committee of 6 officials is to be chosen from 8 men and 7 women. If the committee is to…

A:

Q: A college has 3 entrance gates and 2 exit gates. In how many ways can a student enter then leave the…

A:

Q: If there are 3 roads from Town A to Town B and 4 roads from Town B to Town C, in how many ways can…

A: there are 3 ways to go from A to B  4 ways to go from B to C  3 ways to go from C to B as we can not…

Q: In how many ways can a couple invite 3 out of their 15 closest friends to a dinner party?

A:

Q: how many ways can 2 men, 3 women, 4 boys, and 5 girls be selected from 4 men, 5 women, 6 boys and 7…

A:

Q: (3) In how many ways can 5 boys and 2 girls sit in a row if just the girls are to sit together?

A: Permutation is a method in mathematics that is used to find the number of ways in which certain…

Q: If a family has four children, in how many ways could the parents have two boys and two girls?

A:

Q: Suppose that you must choose three people to meet with a customer. You have nine people to choose…

A: Given data, Total number of people (n)=9 Number of people to meet with a customer (r)=3

Q: 2. In how many ways can three singers and four dancers be chosen to make a team if there are seven…

A: We have to find in how many ways three singers and fours dancers be chosen to make a team if there…

Q: In how many ways can a large retail store select 3 sites on which to build a new store if it has 12…

A: We have to find given combination possible.

Q: Suppose you have 11 books and you randomly pick 3 to take on vacation with you. How many ways can…

A: To count the number of possible selections

Contingency Table

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.

Binomial Distribution

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.