Question

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 committee has no
repetition and order does not matter.

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?

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.

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?

(a) If 25 women compete in the marathon at the Olympics, in how
many different ways can the gold, silver and bronze medals be
awarded?
(b) If a three person committee is chosen at random from a group
of 24 people, how many different committees are possible?
(c) in a new lottery game called "Minibucks", you select four
numbers between 1 and 15. If you match all four numbers with the
four numbers chosen by the lottery that day, you...

At Pizza Hut, a customer wants to buy some pizza. How many
different ways can a customer buy 4 different types of pizzas out
of 11?
a. For this example, what formula will we need to use?
Permutation : n P r = n ! ( n − r ) !
Perumtation Rule #2 : n ! r 1 ! ⋅ r 2 ! ⋅ r 3 ! ⋅ ... ⋅ r p
!
Fundamental Counting Rule : k 1...

Managers of an office selected a committee of five employees to
participate in discussions on how to revise the flow of work in the
office. The office has 25 employees, of which 10 are men. If the
commit- tee is selected at random from the 25 employees, is it
likely to have 4 men? (This question and the follow- ing introduce
the calculations that define a hypergeo- metric random
variable.)
(a) Explain why it would not be appropriate to use...

Do Males have Females have different voting tendencies? In a
recent study, 1000 Men and Women were asked their Voting
Preferences. The results are provided in the two-way contingency
table below. Test to determine if Males and Females are
Independent. If you find significant results, please describe them.
Use α = .05
Voting Preferences
Gender
Republican
Democrat
Independent
Male
200
150
50
Female
250
300
50

Please show your work and provide explanation!
1a) How many different ways can 40 people be divided into two
groups, with at least one person in each group? For example, a
partition can be {1} and {2-49}. Another example of a partition
could be {1-20} and {21-40}. There is no limit to how many people
can be in each group as long as they each have at least one
person.
1b) A deck of cards has 52 cards, 4 suits...

20 women and 30 men between 18 to 60 years old and the
number of hours that they work. These information would be your
populations. For each group find the followings:
20 Women Ages = 19, 23, 40, 18, 60, 50, 21, 30, 33, 28,
33, 35, 28, 24, 28, 18, 19, 22, 25, 50
20 women work hours weekly = 40, 24, 30, 31, 19, 10, 21,
5, 40, 9, 8, 40, 37, 12, 20, 40, 20, 10, 40,...

2. How many ways can you select a planning committee of three
for a group of eight executives
3. You have produced four advertisements to use while selling a
new product. What are all the possible ways you can order these
four ads if you plan to only use two during the summer months
4. A manufacturer of cranes purchases electric motors from three
suppliers: General Electric, Westinghouse, and Samsung. Thirty
percent of the motors are purchased from General Electric,...

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