Question

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?

Answer #1

As only gender is considered, we don't have to distinguish between
the people of same gender.

The total number of arrangements = 9!/(6!*3!) (As 3 men and 6 women
are alike)

= 84 ways

Therefore, six women and three men can gather in a line in 84
ways.

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.

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.)

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...

In how many ways can 16 people stand in a circle?
In how many ways can 16 people stand in a line?
Suppose that 8 of the people are men and 8 are women. In how
many ways can they stand in a circle assuming
that they alternate in gender?
In how many ways can 8 men and 8 women stand in a line,
alternating in gender?

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.

There are 7 women and 5 men in a department. (a) How many ways
can a committee of 4 people be selected if there must be 2 men and
2 women on the committee? (b) If a committee is formed at random,
what is the probability that it is made up of 2 men and 2
women.

Consider 12 people (5 men and 7 women).
1. How many ways are there of forming teams of 5, if the team must
consist of 3 men and 2 women? How many if it must consist of at
least one man? How many if it must contain at most one man?

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...

Suppose that a town has 100 ill people: 25 children, 41 men, and
34 women.
(a) In how many ways can 14 children and 16 women be selected
from this group for transport to the nearest hospital?
(b) Suppose that 14 children and 16 women have been selected and
transported to the hospital, where beds
number 23 to 69 are available for new patients. In how many ways
can they be assigned to beds?
(c) In how many ways can...

A group of 3 men and 3 women went to the movies. How many ways
can you sit in a row of 6 chairs if men want to sit together and
women want to sit together?

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