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: 2. Claire has 100 baseball cards. He wants to place the cards in three stacks so that the second…

A: We need to find number of cards in first,second and third stack We need to find  how many stacks…

Q: A boy owns 10 pairs of pants, 7 shirts, 4 ties, and 8 jackets. (a) How many outfits can he wear to…

A: a) Given that the boy owns 10 pairs of pants, 7 shirts, 4 ties, and 8 jackets. All items are…

Q: 20 professors are having a tea party, 6 physicists and 14 mathematicians. To prepare, they need to…

A: From given data we have : 20 professors are having a tea party, 6 physicists and 14 mathematicians.

Q: A telephone number consists of 10 digits: 3 digit area code followed by 7 digit number. How many…

A: For area code , possible first digits are 1 to 9 and for the other number ,remaining digits are 0-9…

Q: a. In how many ways can 3 civil engineers and 2 mechanical engineers be chosen from the applicants?…

A: Here use combination An Engineers Association has a couple of vacant positions and there are a total…

Q: There are four oranges, five pineapples, and t juice using only two fruits of different types. make…

A: Given: Number of oranges = 4 Number of pineapples = 5 Number of mangoes = 3 Total number of fruits =…

Q: There are 15 married couples in a dressing room. The photographer is tasked to take a picture of…

A: We need to find the number of people who must be called out of the room so that he is sure that…

Q: are possible? (a) How many different delegations The 4 delegates can be selected different ways. (b)…

A: Solution: The total number of delegates to be chosen is 4. The number of available resources to…

Q: Student Painters, which specializes in painting the exterior of residential buildings, has nine…

A: The number of ways r items can be selected from n different items is equal to C(n,r) . The formula…

Q: (i) CarLand is a car dealership with 22 sales staff. They decide to select 8 staff to be trained as…

A: A set of m member staffs from total n members group can be formed in any nm ways, with condition…

Q: A committee of students and teachers is being formed to study the issue of how much they all love…

A: Given: 16 teachers and 35 students Total = 51 members  At least 2 teachers and at least 2 students…

Q: The computer science department has 7 members; the mathematics department has 6 members. We need to…

A: We use combination for selection

Q: A job interviewer has set 10 questions with four answer options and one correct answer. In how many…

A: The number of ways for two events to occur in a sequence is p×q. Here, p is the number of ways the…

Q: There is a group of 8 instructors and 13 new students at a university sports match. They wish to…

A: Given that there are 8 instructors and 13 new students at a university sports match. So total…

Q: 7. A computer programming team has 15 members consisting of eight humans and seven robots. A…

A: 7. Given that a computer programming team has 15 members consisting of 8 humans and 7 robots. Also,…

Q: A group of nine women and four men must select a four-person committee. How many committees are…

A: Choose the 2 women 9C2 = 36 ways. Choose the 2 men 4C2 = 6 ways Tats 36*6 = 216 ways.

Q: A small university has 5 academic departments. A committee of 3professors is going to be formed,…

A: Given that a small university has 5 academic departments namely, Art department, History, Dance,…

Q: Prove by induction that 1 2. Prove that (xn) is contractive and thus convergent. Compute lim (xn).

A:

Q: How many students are taking at least one of the three classes?

A: Concept:   The number of ways of achieving success that is the total number of possible outcomes is…

Q: A group of 150 tourists planned to visit East Africa. Among them, 3 fall ill and did not come, of…

A: Consider the provided question, First draw the Venn diagram according to the given question, Let K…

Q: A boy owns 10 pairs of pants, 6 shirts, 2 ties, and 9 jackets. (a) How many outfits can he wear to…

A: Multiplication rule of counting: If a task consists of a sequence of choices in which there are ‘a’…

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

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

Q: 10 people are in a club. How many ways are there to form a committee consisting of members of the…

A: 1. Number of ways to form a committee consisting of members of the club such that the committee has…

Q: The cafeteria is serving french toast, cereal, and fruit. If a student may choose any two of those…

A:

Q: . How many different ways are there of handing out the prizes if (a) the prizes are all the same?…

A: A kindergarten class has 18 children. FIve of the children are selected to receive prizes. Here use…

Q: A town is forming a committee to investigate ways to improve public safety in the town. The…

A:

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

A:

Q: Suppose that a department contains 9 women and 15 men. How many ways are there to form a committee…

A: Given:Total women = 9Total men = 15Total committee members required = 7Condition: The committee must…

Q: A large research project is looking for more researchers. There are 8 spots open on the research…

A:

Q: Los Angeles Dodgers. From the official website of the 2013 Los Angeles Dodgers major league baseball…

A: Given info:Five active players available on roster to play outfield.

Q: A co-rec team to play in an intramural tournament of indoor soccer should consist of three men and…

A: Let us suppose there are three marbles viz. a red, a green and a blue. From these, there are three…

Q: Jessica is grocery shopping and has 16 cherry tomatoes and 12 grape tomatoes in her shopping basket.…

A:

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.