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?

Q: How many different committees are possible that consist of 5 women and 3 men selected from a group…

A: For a committee, arrangement does not matter so use the combination method.  We can select 5 women…

Q: A committee has 20 people.  In how many ways can a President, Vice-President, and Secretary be…

A: Note:  Permutation: We kno that, nPr represents the selection an ordered set of ‘r’ objects from a…

Q: In how many ways can a committee of three men and two women from eight men and six women

A: given data  make committee of 3 men and 2 womens from 8 mens and 6 womens.

Q: Three research department have 8,6,and 10 members , 4 respectively. Each department is to select a…

A: Three research department have 8,6, and 10 members, respectively.

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 committee is to be formed consisting of 4 men and 5 women. If the committee members are to be…

A: Answer  Given  A committee is to be formed consisting of 4 men and 5 women. If the committee members…

Q: The qualified applicant pool for five management trainee positions consists of six women and five…

A: According to the provided information,  6 woman and 5 man  Total number of members = 11 5 management…

Q: How many ways can a delegation of 55 Republicans, 55 Democrats, and 22 Independents be selected from…

A: Given data Number of Republicans = 77 Number of Democrats = 77 Number of Independent = 33

Q: How many committees of six can be formed from 17 Republicans and 14 Democrats if three members of…

A: Given : 17 Republicans and 14 Democrats

Q: Assume that there are 105 students: 45 of which like rock, 52 of which like country, and 23 of which…

A:

Q: How many different committees can be formed from 11 teachers and 42 students if In how many ways can…

A:

Q: A boyscout troop has 10 members. a. How many ways can the Troup Leader select 3 members to lead a…

A: Given A boy scout troop has 10 members. To find a. How many ways can the Troup Leader select 3…

Q: The qualified applicant pool for three management trainee positions consists of seven men and six…

A: Given, The qualified applicant pool for 3 management Trainee positions consist of 7 men and 6…

Q: How many ways are there to select the 5-person committee such that exactly 3 local business owners…

A: It is given that Total persons = 20 Number of homeowners = 11 Number of local businesses owners = 20…

Q: suppose that we wish to seat 10 people, 5 men and 5 women, in a row of ten chairs. in how many ways…

A:

Q: How many different teams of 4 members can be selected from a pool of 20 applicants?

A: The combination formula is given by

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

A:

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: 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: