Question

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.

Answer #1

Suppose that a department contains 11 men and 16 women. How many
ways are there to form a committee with 6 members if it must have
strictly more women than men?

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...

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?

1. In how many ways can 10 objects be split into two
groups containing 4 and 6 objects, respectively?
2. In how many ways can a committee of 5 people be chosen out of 9
people?
3. Out of 5 mathematicians and 7 physicists, a committee consisting
of 2 mathematicians and 3 physicists is to be formed. In how many
ways can this be done if (a) any mathematician and any physicist
can be included, (b) one particular physicist must...

10 men and 5 women are meeting in a conference room. Four people
are chosen at random from the 15 to form a committee.
a) What is the probability that the committee consists of 2 men
and 2 women?
b) Among the 15 is a couple, Bob and Jane. What is the
probability that Bob and Jane both end up on the committee?
c) What is the probability that Bob ends up on the committee but
Jane does not?

A committee of 5 persons is to be selected out of 6 men and 2
women. Find the number of ways in which more men are selected than
women? b) If 5 students are to be randomly chosen from a group of
12 students to form a committee for a class trip, what is the
probability that group members Alice and Tom will be chosen for the
committee?

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?

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 committee of 4 people is chosen from 9 women and 9 men. How
many different committees are possible that consist of 2 women and
2 men?

For this problem, assume that the committee contains 9 men and 5
women and that three are selected at random for a subcommittee.
What is the probability that the subcommittee consists of 2 men and
1 woman, given that it contains both men and women?

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