A computer programming team has 15 members consisting of eight robots and seven humans. A committee of exactly 7 of these team members must be put together to work on bug testing. You may leave your answer unreduced. (a)How many committees can be chosen that contain exactly four robots and three humans? (b) How many committees can be chosen that contain at most two robots? (c) How many committees can be chosen that contain at least one human?

Q: A pharmaceutical company recently hired 5 biologists, 3 chemists, 4 environmental scientists, and 3…

A:

Q: 1. A girl has 6 bags, 11 dresses and 7 pairs of shoes. On how many different ways can she dress up?…

A:

Q: Both of my friends Abu and Deps will be part of the group? Only one of them will be part of the…

A: Here use combination for given problems

Q: how many ways can the 30 members of a company club select a president, a vice president, and a…

A: From the given information we find the solution.

Q: An organization has 15 members, 5 of whom are analysts, 3 of whom are chemists and the rest are…

A: Combination only includes number of ways of selection whereas, permutation includes number of ways…

Q: There are 5 third year and 4 fourth year students qualified to join a contest. In the group…

A: Given that there are 5 third year and 4 fourth year students qualified to join a contest. In the…

Q: A team composed of two grade 11 and two grade 10 students is to be sent to a debate contest. If…

A: The provided information is  There are Two grade 11 and two grade 10 students  There are also 60…

Q: A senate committee has 15 members.  If a subcommittee of 6 senators is to be formed from the…

A:

Q: Out of 8800 kids visited a restaurant, 2400 like pizza, 3360 like burgers, and 2240 like sandwich,…

A:

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

A:

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

A: Topic:- permutation and combinations

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: For the new fall season, a network president has 11 shows in development, and 8 openings in the…

A: The network president has 11 shows in development . There are eight openings in the prime time…

Q: A certain congressional committee consists of 8 senators and 12 representatives. How many ways can a…

A: It is given the number of senators is 8 and representatives is 12.

Q: The Raiders and Cowboys have each made up a scouting list. There are 25 players on the Raiders' list…

A:

Q: you had a box of five different kinds of fruit and you could choose 2, you might get an apple and an…

A: Given that  Number of types of fruits (n) = 5 Number of fruits we could choose = 2   We know that…

Q: Seven women and nine men are on the faculty in the mathematics department at a school.   1. How…

A:

Q: box with a square base and no top is to be made from a square piece of tin by cutting out a 3-inch…

A: Given, Square base No top Volume= 48 cubic inches

Q: If it will be allowed to use a number repeatedly, how many 4-digit numbers can we form from the…

A: In this question we have to find how many four digit can be formed from the given numbers.

Q: If I go into an ice cream parlor, and I have the choice of having one of 10 different flavors, with…

A: Combination:  If you don’t care what order you have things then it’s a combination. Think of Lottery…

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: group of 9 grade 11’s and 13 grade 12’s apply to go to a student conference in Vancouver, but there…

A:

Q: Out of 5 class representatives and 7 prefects, a committee consisting of 2 class representatives and…

A:

Q: In a certain state, all car license plates have four capital letters followed by three digits.…

A:

Q: How many ways are there to select the 5-person committee such that exactly 2 local business owners…

A: We have given that  Total number of volunteers = 20 Number of homeowners = 11 Number of local…

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

A:

Q: there are 651 6th grade students at a school, and three out of every seven of them play a sport, how…

A: Given   Number of 6th grade students : 651   If 3/7 plays sports,    Then who don't play a sports…

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

A: Given information Letter can start with letter K or W and include either two or three additional…

Q: To fill a number of vacancies, the personnel manager of a company has to choose three secretaries…

A: The number of ways a company has to choose three secretaries from among ten applicants can be done…

Q: f any arrangement of letters is considered a word, and there are 21 consonants and 5 vowels to…

A:

Q: From a group of 4 men and 5 women, how many committees of size 3 are possible a) With no…

A: Note: Hi, thank you for the question. As per our company guideline we are supposed to answer only…

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: Delegates from 10 countries, including Russia, France, England, and the United States, are to be…

A: Given  10 countries in total  4 of them are Russia, France, England, United States  We need to…

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 ways of choosing ten students from a class of twenty-five is the same as the number of…

A: So in this we have to find the both then evaluate to see both are same so for this I'm providing…

Q: From a group of 10 men and 5 women, how many committees of size 5 are possible? a.) With no…

A: Given From a group of 10 men and 5 women, how many committees of size 5 are

Q: A local radio station took a poll of 90 of its listeners to find out whether they like to watch…

A: let M be the listeners who like mariners games SE be the listeners who like seahawks games, SO be…

Q: A student taking an examination is required to answer exactly 10 out of 15 questions. in how many…

A:

Q: A company has 10 software engineers and 6 civil engineers. In how many ways can they be seated…

A:

Q: 1. A college freshman must take a science course, a humanities course, and a mathematics course. If…

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: A veterinarian surveys 28 of his patrons.  He discovers that 12 have dogs, 10 have cats, and 6 have…

A:

Q: A teacher and his eleven students are standing in a single file line waiting to enter the cafeteria…

A: We have given that a teacher and his eleven students are standing in a single file line waiting to…

Q: A university student is selecting courses for his next semester. He can choose from 6 science…

A:

Q: Suppose that a department contains 10 men and 15 women. How many ways are there to select a…

A:

Q: 6. If there are 12 teams in a basketball tournament and each team must play every other team in the…

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: A computer programming team has 17 members. Suppose nine team members are women and eight are men.…

A: 1] There are 17 members in the team 2] Out of which 9 team members are women and 8 are men

Q: In the United States, telephone numbers consist of a three-digit area code followed by a seven digit…

A:

Q: A student club consists of 9 freshmen and 9 sophomores. • How many different six-person committees…

A: use permutation and combination find the solution

Counting Principles

In statistics, the counting principle can be said to be the concept in which the quantity of an item is determined. There can be a single item, or a group of items, or items that are related to each other. In every possible set of items, the quantity of the possible item groups or their sorting measures can be determined with counting principles.