Example 9: A department has 30 members and a committee of 5 people is needed to
ID: 2931136 • Letter: E
Question
Example 9: A department has 30 members and a committee of 5 people is needed to carry out a task. How many different possible committees are there? Example 10: A department has 30 members and a committee is needed to carry out a task. The committee is to be composed of a chairperson and four members. How many different possible committees are there? N (committees : the number of ways to choose a chairperson number of ways to choose 4 members out of 29 Example 11: A department has 30 members and a committee is needed to carry out a task. The committee is to be composed of two co-chairpersons and three members. How many different possible committees are there? Example 12: In how many ways can 8 people be selected from 10 volunteers for a drug study?Explanation / Answer
9. Since there are 30 committees and 5 people need to be selected, number of committees possible
= 30C5.
10. There are 30 people and the number of ways to choose the chairperson = 30.
Once the chairperson is chosen, there are 29 people left.
Four members can be chosen out of 29 in 29C4 ways.
=> Number of ways to choose the committtee = 30 * 29C4.
11. The two chairpersons can be chosen out of 30 in 30C2 ways.
Once the 32 people are chosen, three members can be chosen out of the remaining 28 in 28C3 ways.
=> Number of ways to form the committee = 30C2 * 28C3.
12. The number of ways to select 8 volunteers out of 10 = 10C8
= 10! / (8! * (10-8)!)
= 10! / (8! 2!)
= 10*9/2 = 45.
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.