# 0.11 Sets and counting: homework  (Page 5/5)

 Page 5 / 5

A coin is tossed 10 times, in how many ways is it possible to get seven heads and three tails?

How many subsets are there of a set that has 6 elements?

64

How many subsets are there of a set that has $n$ elements?

## Chapter review

Suppose of the 4,000 freshmen at a college everyone is enrolled in a mathematics or an English class during a given quarter. If 2,000 are enrolled in a mathematics class, and 3,000 in an English class, how many are enrolled in both a mathematics class and an English class?

1,000

2. How many had read Time or Newsweek but not the U. S. News And World Report?

1. 20
2. 135
3. 15

At a manufacturing plant, a product goes through assembly, testing, and packing. If a plant has three assembly stations, two testing stations, and two packing stations, in how many different ways can a product achieve its completion?

12

Six people are to line up for a photograph. How many different lineups are possible if three of them insist on standing next to each other ?

144

How many four-letter word sequences can be made from the letters of the word CUPERTINO?

3,024

In how many different ways can a 20-question multiple choice test be designed so that its answers contain 2 A's, 4 B's, 9 C's, 3 D's, and 2 E's?

11,639,628,000

The U. S. Supreme Court has nine judges. In how many different ways can the judges cast a six-to-three decision in favor of a ruling?

84

In how many different ways can a coach choose a linebacker, a guard, and a tackle from five players on the bench, if all five can play any of the three positions?

60

How many three digit even numbers can be formed from the digits 1, 2, 3, 4, 5 if no repetitions are allowed?

24

Compute:

1. $9C4$
2. $8P3$
3. $\frac{\text{10}!}{4!\left(\text{10}-4\right)!}$
1. 126
2. 336
3. 210

In how many ways can 3 English, 3 Math, and 4 Spanish books be set on a shelf if the books are grouped by subject?

5,184

In how many ways can a 10-question multiple choice test with four possible answers for each question be answered?

1,048,576

On a soccer team three fullbacks can play any of the three fullback positions, left, center, and right. The three halfbacks can play any of the three halfback positions, the four forwards can play any of the four positions, and the goalkeeper plays only his position. How many different arrangements of the 11 players are possible?

46,200

From a group of 6 people, 3 are assigned to cleaning, 2 to hauling and one to garbage collecting. How many different ways can this be done?

60

How many three-letter word sequences can be made from the letters of the word OXYGEN?

120

In how many ways can 3 books be selected from 4 English and 2 History books if at least one English book must be chosen?

20

Five points lie on the rim of a circle. Choosing the points as vertices, how many different triangles can be drawn?

10

A club consists of six men and nine women. In how many ways can a president, a vice president and a treasurer be chosen if the two of the officers must be women?

1296

Of its 12 sales people, a company wants to assign 4 to its Western territory, 5 to its Northern territory, and 3 to its Southern territory. How many ways can this be done?

27,720

How many permutations of the letters of the word OUTSIDE have consonants in the first and last place?

720

How many distinguishable permutations are there in the word COMMUNICATION?

194,594,400

How many five-card poker hands consisting of the following distribution are there?

1. A flush(all five cards of a single suit)

2. Three of a kind(e.g. three aces and two other cards)

3. Two pairs(e.g. two aces, two kings and one other card)

4. A straight(all five cards in a sequence)

1. 5148
2. 58,656
3. 123,552
4. 10,240 or 9216

Company stocks on an exchange are given symbols consisting of three letters. How many different three-letter symbols are possible?

17,576

How many four-digit odd numbers are there?

4500

In how many ways can 7 people be made to stand in a straight line? In a circle?

5040; 720

A united nations delegation consists of 6 Americans, 5 Russians, and 4 Chinese. Answer the following questions.

1. How many committees of five people are there?

2. How many committees of three people consisting of at least one American are there?

3. How many committees of four people having no Russians are there?

4. How many committees of three people have more Americans than Russians?

5. How many committees of three people do not have all three Americans?

1. 3003
2. 371
3. 210
4. 191
5. 435

If a coin is flipped five times, in how many different ways can it show up three heads?

10

To reach his destination, a man is to walk three blocks north and four blocks west. How many different routes are possible?

35

All three players of the women's beach volleyball team, and all three players of the men's beach volleyball team are to line up for a picture with all members of the women's team lined together and all members of men's team lined up together. How many ways can this be done?

72

From a group of 6 Americans, 5 Japanese and 4 German delegates, two Americans, two Japanese and a German are chosen to line up for a photograph. In how many different ways can this be done?

72,000

Find the fourth term of the expansion ${\left(2x-3y\right)}^{8}$ .

$-\text{48384}{x}^{5}{y}^{3}$

Find the coefficient of the ${a}^{5}{b}^{4}$ term in the expansion of ${\left(a-2b\right)}^{9}$ .

$\text{2016}{a}^{5}{b}^{4}$

How we are making nano material?
what is a peer
What is meant by 'nano scale'?
What is STMs full form?
LITNING
scanning tunneling microscope
Sahil
what is Nano technology ?
write examples of Nano molecule?
Bob
The nanotechnology is as new science, to scale nanometric
brayan
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Damian
Is there any normative that regulates the use of silver nanoparticles?
what king of growth are you checking .?
Renato
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
why we need to study biomolecules, molecular biology in nanotechnology?
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
why?
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
anyone know any internet site where one can find nanotechnology papers?
research.net
kanaga
sciencedirect big data base
Ernesto
Introduction about quantum dots in nanotechnology
what does nano mean?
nano basically means 10^(-9). nanometer is a unit to measure length.
Bharti
do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
absolutely yes
Daniel
how to know photocatalytic properties of tio2 nanoparticles...what to do now
it is a goid question and i want to know the answer as well
Maciej
Abigail
for teaching engĺish at school how nano technology help us
Anassong
How can I make nanorobot?
Lily
Do somebody tell me a best nano engineering book for beginners?
there is no specific books for beginners but there is book called principle of nanotechnology
NANO
how can I make nanorobot?
Lily
what is fullerene does it is used to make bukky balls
are you nano engineer ?
s.
fullerene is a bucky ball aka Carbon 60 molecule. It was name by the architect Fuller. He design the geodesic dome. it resembles a soccer ball.
Tarell
what is the actual application of fullerenes nowadays?
Damian
That is a great question Damian. best way to answer that question is to Google it. there are hundreds of applications for buck minister fullerenes, from medical to aerospace. you can also find plenty of research papers that will give you great detail on the potential applications of fullerenes.
Tarell
what is the Synthesis, properties,and applications of carbon nano chemistry
Mostly, they use nano carbon for electronics and for materials to be strengthened.
Virgil
is Bucky paper clear?
CYNTHIA
carbon nanotubes has various application in fuel cells membrane, current research on cancer drug,and in electronics MEMS and NEMS etc
NANO
how did you get the value of 2000N.What calculations are needed to arrive at it
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If March sales will be up from February by 10%, 15%, and 20% at Place I, Place II, and Place III, respectively, find the expected number of hot dogs, and corn dogs to be sold
8. It is known that 80% of the people wear seat belts, and 5% of the people quit smoking last year. If 4% of the people who wear seat belts quit smoking, are the events, wearing a seat belt and quitting smoking, independent?
Mr. Shamir employs two part-time typists, Inna and Jim for his typing needs. Inna charges $10 an hour and can type 6 pages an hour, while Jim charges$12 an hour and can type 8 pages per hour. Each typist must be employed at least 8 hours per week to keep them on the payroll. If Mr. Shamir has at least 208 pages to be typed, how many hours per week should he employ each student to minimize his typing costs, and what will be the total cost?
At De Anza College, 20% of the students take Finite Mathematics, 30% take Statistics and 10% take both. What percentage of the students take Finite Mathematics or Statistics?