1)Tom has 2021 balloons to be evenly distributed among 21 students. If every student receives the same number of balloons, how many will each student receive? Will there be any balloons left over?

Q: 1.A contractor wishes to build 9 houses, each different in design. In how many ways can he place…

A: A permutation is a mathematical technique that determines the number of possible arrangements in a…

Q: Suppose we want to choose 4 objects, without replacement, from 18 distinct objects. (a) How many…

A: Permutations and combinations

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

A:

Q: Assume that the committee has 14 members, and that 4 different members are to be given special…

A: We have to find probability..

Q: The 13 colleges of interest to a high school senior include 4 that are expensive (tuition more than…

A:

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: In how many different ways can the director of a research laboratory choose two chemical engineers…

A:

Q: A race has 10 runners. In how many ways can the first three places be decided?

A: Here use combination

Q: In how many ways can 12 different books be distributed among four chil- dren so that (a) each child…

A:

Q: What is the minimum number of students required in a discrete mathematics class to be sure that at…

A: We solve the given problem in next step.

Q: In a friend group of six, how many ways can we arrange them in a line for a photograph?

A: In a friend group of six, we have to arrange them in a line for a photograph.

Q: In how many ways can a comittee of 6 be chosen from 6 administrators and 4 supervisors if all are…

A:

Q: The State of Georgia is distributing $200 million in funding to Fulton, Bibb, Gwinnett, DeKalb,…

A: Given that total funding is 200 million dollars and each country receives at least 2 million…

Q: A child has 25 blocks, of which 8 are yellow, 4 are red, 6 are green, 4 orange, and 3 are blue. If…

A: Given, A child has 25 blocks, of which 8 are yellow, 4 are red, 6 are green, 4 orange, and 3 are…

Q: Suppose a car you want to buy has five choices for inte-rior colors, three types of radios, three…

A: Given Data: The number of choices for interior colours is: N1=5 The number of choices for radios is:…

Q: Suppose we want to choose 6 objects, without replacement, from 10 distinct objects. (a) How many…

A: We can find answer to both the question as below

Q: A committee of 5 delegates is to be chosen from a group of 17 delgates, 10 of whom are women. If at…

A: If an event can be done in n different ways and if another even can be done in m number of ways,…

Q: 1. If Peter Piper picks 4 baskets of peppers on day one, 7 baskets on day two, and each day…

A: 1. Given peter Piper picks 4 baskets on day 1, 7 on day 2 and 3 more than the previous day…

Q: In how many ways can a committee of not more than 3 representatives be selected from a group of 16…

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: 5. How many arrangements can be made from 4 boys and 4 girls if they have to sit in a roundtable and…

A: We have given that  Number of boys=4 Number of girls=4

Q: In how many ways can an HR department head choose one or more applicants from six eligible…

A: Number of eligible applicants=6Choose one or more applicants Let, Number of ways=n=?

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: In how many ways can 7 students from a class of 28 be chosen for a field trip?

A:

Q: 1. In how many ways: a. Can 8 people be lined up to get on a bus? b. Can they be seated if 4…

A:

Q: Suppose a club has 20 members. a. How many ways can they select a chairperson to lead a small…

A: Since you have asked a question with multiple parts in a single request, we would be answering only…

Q: How many ways are there to distribute eight different toys among four children if the first child…

A:

Q: 2.27 A developer of a new subdivision offers a prospective home buyer a choice of 4 designs, 3…

A: Generalized multiplication rule: The number of ways of performing sequence of k operations is…

Q: 4. A computer center acquires eight different models of laptops of the same color and shape. If they…

A: We have in all 8 laptops in a drawer and choose 5 from them.

Q: A collection of eight blue blocks and seven red blocks, all with distinct shapes, are to be lined up…

A: When the blocks are lined up, their position can be marked up as   (1) (2) (3). . . . . . . (15)  As…

Q: 4. A committee of 6 officials is to be chosen from 8 men and 7 wor If the committee is to contain at…

A:

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: (1) How many ways are there to pick a 5–person basketball team from 14 possble players? (ii) How…

A: In this question, we have to use the method of permutation and combination to answer the following…

Q: In how many ways can we distribute 10 indistinguishable oranges and 1 tangerine among 3 children…

A:

Q: (a) How many committees can be formed? (b) How many committees can be formed with at least 2 men?…

A: here total 8 men and 7 women that is 15 employees in office committee of 4 member has to be formed…

Q: if a coin is tossed 4 times, and then a standard 6 sided die is rolled 4 times and a group of 3…

A: Given Coin is tossed. 4 times  Standard 6 sided die. Rolled 4 times  Group of 3 cards drawn  without…

Q: A2. a. A company decided to distribute 5 identical computers among its employees. In how many…

A: The number of identical computers is 5. The number of distinct people is 3. Since, each employee…

Q: 1. In how many ways may 4 people be seated in a row of 10 chairs? 2. In how many ways can a point…

A: HERE use permutation and combination

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 nine students be partitioned into three teams containing four, three, and two…

A:

Q: A committee of size 5 is to be chosen from a group of 6 men and 7 women. (a) How many different…

A: Given that 6 men and 7 women. Total people = 6 + 7 = 13

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

A:

Q: 1. There is a deck of 52 cards. How many ways are there to distribute 13 cards to each of 4 players?

A:

Q: Given six distinct pairs of gloves, 12 distinct gloves in all, how many ways are there to distribute…

A:

Q: 1. A license plate begins with three letters and three numbers. If the possible letters are all…

A: Given: The possible letters are vowels; that is, a, e, i, o, u. The possible digits are odd numbers;…

Q: 4. Consider a bag containing four red marbles, two green ones, one transparent one, three yellow…

A: Given that there are 4 red marbles, 2 green,1 transparent, 3 yellow, and 2 orange marbles. So there…

Q: If 6 out of 30 people over the age of 100 are male, Ho our of 30 people over the age of 100 are…

A: Given that The number of total people=30 Number of male over aged of 100 =6 Then we have to find the…

Q: Suppose an organization elects its officers from a board of trustees. If there are 52 trustees, how…

A: Given: Number of trustees = 52 Board has to elect a president, vice-president, secretary, vice…

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.

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.