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- A club has 11 members. Five are to be chosen to go as a group to a national meeting. If the club contains 7 men and 4 women, how many distinct groups of five contain at most two women?Faculty at a certain university need to create a committee to evaluate the general studies curriculum offered on campus. If there are 25 faculty members and they must select a chair, vice chair, secretary and 4 additional faculty members to be on the committee, in how many ways can the committee be formed?1. In a house of 10 people, how many ways can a squad of 4 people be arranged? 15 participants have written their names on small sheets of paper for a raffle. Show different ways on how the three names will be chosen. 2. 3. School is over, your family is planning a vacation somewhere outside the city, and your mom is letting you bring your five favorite books. Suppose there are 12 total books (including academic books, history books), how many different ways can you choose the five books? 4. On a circle there are 24 points selected. How many squares with edges in these points exist? 5. On the plane there are 6 different points (no 3 of them are lying on the same line). By joining all the points, how many segments do you get?
- Suppose that a drama class has 22 students. a. In how many ways can four students be selected to take part in a survey? b. In how many ways can four students be selected to act out a scene from a play involving 4 different parts?3.A senior high school has, 5,000 students enrolled for academic year 2016-2017. Of these, 1200 are majoring STEM, 1,500 are ABM, 700 are HUMSS, and the remaining are GAS. A.What percent of the enrollees take HUMSS? B.What percent has chosen a major which is not HUMSS or ABM? C.What percent are enrolled to GAS?If there are three routes from Detroit to Chicago and 8 routes from Chicago to Michigan, how many different routes may be taken in going to Detroit to Michigan via Chicago? Answer. 24 ways
- f) Student council needs to create a committee of 6 students to run their social events. 12 students applied to be on the committee, 8 women and 4 men. The committee must have at least 1 woman and at least 1 man. How many ways can the committee be selected?A research team of 7 members must be formed from a group of 10 teachers consisting of 3 senior faculty, 4 junior faculty and 3 rookie faculty members. a. In how many ways can the selection be done if the team must include at least 1 senior faculty member? b. In how many ways can the selection be done if the team must include 2 seniors and at least 1 rookie faculty member?3. A company checks its managers and find that 70 of them have an undergraduate degree in Business, 30 have an undergraduate degree in business and a Masters in Business, and 45 have only A Masters in Business. 20 others have neither degree. How many managers are in this company?