Concept explainers
Selecting a Committee There are 7 women and 5 men in a department. How many ways can a committee of 4 people be selected? How many ways can this committee be selected if there must be 2 men and 2 women on the committee? How many ways can this committee be selected if there must be at least 2 women on the committee?
The number of ways to select 4 people for the committee, 2 men and 2 women for the committee and at least 2 women for the committee.
Answer to Problem 43E
There are 495 ways to select 4 people out of 12 people.
There are 210 ways to select 2 men and 2 women
There are 420 ways to select at least 2 women.
Explanation of Solution
Given info:
A committee must be formed with 4 members. There are 7 women and 5 men available for the selection.
Calculation:
Combinations:
A combination is an arrangement of n objects in r ways where the order of arrangement is not considered.
Where, n is the total number of objects and r is number of ways in which n objects can be selected.
The number of ways to select 4 people out of 12 people:
Substitute n as 12 and r as 4.
Thus, there are 495 ways to select 4 people out of 12 people.
The number of ways to select 2 women and 2 men out of 7 women and 5 men:
Substitute n as 7 and r as 2.
Thus, there are 21 ways to select 2 women out of 7 women.
Substitute n as 5 and r as 2.
Thus, there are 10 ways to select 2 men out of 5 men.
Fundamental counting rule:
The number of ways in which a sequence of n events occur if the first event can occur in
The number ways to select 2 men and 2 women is given below:
Thus, there are 210 ways to select 2 men and 2 women.
The number of ways to select at least 2 women for the committee:
There can be 2 women, 3 women and 4 women in the committee.
The number of ways to select 2 women and 2 men is 210 ways.
The number of ways to select 3 women and 1 man
Substitute n as 7 and r as 3.
Thus, there are 35 ways to select 3 women out of 7 women.
Substitute n as 5 and r as 1.
The number ways to select 2 men and 2 women is given below:
Thus, there are 175 ways to select 3 women and 1 man.
The number of ways to select 4 women and 0 men
Substitute n as 7 and r as 4.
Thus, there are 35 ways to select 4 women out of 7 women.
The number of ways to select at least 2 women for the committee is given below:
Thus, there are 420 ways to select at least 2 women for the committee.
Want to see more full solutions like this?
Chapter 4 Solutions
Elementary Statistics: A Step By Step Approach
- How many ways can 4 men and 4 women stand in line if all the women are first?arrow_forwardHow many ways can a committee of 3 freshmen and 4 juniors be formed from a group of 8 freshmen and 11 juniors?arrow_forwardA palette of water color paints has 3 shades of green, 3 shades of blue, 2 shades of red, 2 shades of yellow, and 1 shade of black. How many ways are there to choose one shade of each color?arrow_forward
- There are 10 applicants for three sales positions at a department store. All of the applicants are qualified. In how many ways can the department store fill the three positions?arrow_forwardA family consisting of 2 parents and 3 children is to pose for a picture with 2 family members in the front and 3 in the back a. How many arrangements are possible with no restrictions? b. How many arrangements are possible if the parents must sit in the front? C. How many arrangements are possible if the parents must be next to each other?arrow_forwardIn a group of 20 musicians, 12 play piano, 7 play trumpet, and 2 play both piano and trumpet. How many musicians play either piano or trumpet?arrow_forward
- College Algebra (MindTap Course List)AlgebraISBN:9781305652231Author:R. David Gustafson, Jeff HughesPublisher:Cengage Learning
- College AlgebraAlgebraISBN:9781305115545Author:James Stewart, Lothar Redlin, Saleem WatsonPublisher:Cengage LearningGlencoe Algebra 1, Student Edition, 9780079039897...AlgebraISBN:9780079039897Author:CarterPublisher:McGraw HillHolt Mcdougal Larson Pre-algebra: Student Edition...AlgebraISBN:9780547587776Author:HOLT MCDOUGALPublisher:HOLT MCDOUGAL