Question

Six men and six women are to be divided into three different groups, each consisting of two women and two men. In how many ways can this be done? (Answer is 8100)

Explain please.

Answer #1

Number of ways to select r items from n, nCr = n!/(r! x (n-r)!)

Number of ways in which 2 men and 2 women can be selected for first group = 6C2 x 6C2

= 15 x 15

= 225

Number of ways in which 2 men and 2 men can be selected for second group from remaining 4 men and 4 women = 4C2 x 4C2

= 6 x 6

= 36

Number of ways in which 2 men and 2 men can be selected for second group from remaining 2 men and 2 women = 2C2 x 2C2

= 1

Number of ways in which six men and six women can be divided into three different groups, each consisting of two women and two men = 225 x 36 x 1

= **8100**

The qualified applicant pool for three management trainee
positions consists of six women and six men.
(a) How many different groups of applicants can be selected for
the positions?
(b) How many different groups of trainees would consist entirely
of women?
(c) Probability extension: If the applicants are equally
qualified and the trainee positions are selected by drawing the
names at random so that all groups of three are equally likely,
what is the probability that the trainee class will...

six women and three men line up at the.check out
counter at a store. in how many ways can they line up if we
consider only their gender?

An organization consisting of 27 women and 17 men needs to
select from its ranks a committee of 6 people. In how many possible
ways can the committee be formed so that it contains exactly two
men?

The qualified applicant pool for four management trainee
positions consists of six women and five men.
(a) How many different groups of applicants can be selected for
the positions?
(b) How many different groups of trainees would consist entirely of
women?
(c) Probability extension: If the applicants are equally
qualified and the trainee positions are selected by drawing the
names at random so that all groups of four are equally likely, what
is the probability that the trainee class will...

A group consists of seven men and six women. Five people are
selected to attend a conference.
a. In how many ways can five people be selected from this group
of thirteen?
b. In how many ways can five women be selected from the six
women?
c. Find the probability that the selected group will consist of
all women.
(Type an integer or a simplified fraction.)

A jury consists of six men and seven women. Five are selected at
random for an interview. a) Find the number of ways that all
selected people are men. b) Find the number of ways that three men
and two women are selected.

A department is composed of 10 men and 15 women. How many
different ways can a committee be created?
e with 6 members if:
(i) the committee do you have the same number of men as women?
(Count how to choose the
women, then how to choose men and use the Product Rule)
(ii) Do you have more women than men? (There are three cases,
calculate them and use the Sum Rule)
(iii) Explain why the tasks of creating a...

The qualified applicant pool for three management trainee
positions consists of eight women and four men.
(a) How many different groups of applicants can be selected for
the positions?
(b) How many different groups of trainees would consist entirely
of women? (
c) Probability extension: If the applicants are equally
qualified and the trainee positions are selected by drawing the
names at random so that all groups of three are equally likely,
what is the probability that the trainee class...

4 people are to be chosen from 10 men and 12 women to form a
committee which contains at least two women. How many different
ways can the committee be formed? If, among the 10 men and 12
women, Mr. and Mrs. Smith can not both be selected, then how many
different ways can the committee be formed?

A pool of possible jurors consists of 14 men and 16 women.
How many different juries consisting of 5 men and 7 women are
possible?

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 7 minutes ago

asked 45 minutes ago

asked 1 hour ago

asked 1 hour ago

asked 2 hours ago

asked 2 hours ago

asked 2 hours ago

asked 2 hours ago

asked 2 hours ago

asked 2 hours ago

asked 2 hours ago

asked 3 hours ago