Question

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?

Answer #1

A committee of 5 will be chosen from a group of 4 men and 6
women. What is the probability that at least 3 men are chosen?

If a committee of 6 is being selected from a group of 10 men and
12 women, in how many ways can this committee be arranged if at
least 3 must be women?

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.) A committee of five people is to be selected from a group of
11 people. Five of the 11 people are men and the rest are women. If
a committee is randomly selected, find the probability that the
committee has no men.
b.) Given a committee of 5 people, how many ways can we choose
one of these five people to be the chair of the committee and one
of these five people be chosen as the co-chair of...

Five persons are chosen at random from a group of ten persons
consisting of four men and six women. Calculate the probability
that there are more women chosen than men.

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 subcommittee is randomly selected from a committee of eight
men and seven women. What is the probability that all three people
on the subcommittee are 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?

what is the probability that the committee of 7 persons from
group of 6 woman and 5 men has at least 4 woman?

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...

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