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

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

64

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How many subsets are there of a set that has n size 12{n} {} elements?

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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

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In a survey of 250 people, it was found that 125 had read Time magazine, 175 had read Newsweek, 100 had read U. S. News, 75 had read Time and Newsweek, 60 had read Newsweek and U. S. News, 55 had read Time and U. S. News, and 25 had read all three.

  1. How many had read Time but not the other two?

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

  3. How many had read none of these three magazines?

  1. 20
  2. 135
  3. 15
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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

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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

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

3,024

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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

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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

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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

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

24

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Compute:

  1. 9C4 size 12{9C4} {}
  2. 8P3 size 12{8P3} {}
  3. 10 ! 4 ! 10 4 ! size 12{"10"!4! left ("10" - 4 right )!} {}
  1. 126
  2. 336
  3. 210
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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

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

1,048,576

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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

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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

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

120

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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

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

10

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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

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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

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

720

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How many distinguishable permutations are there in the word COMMUNICATION?

194,594,400

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

17,576

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How many four-digit odd numbers are there?

4500

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

5040; 720

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

10

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

35

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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

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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

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Find the fourth term of the expansion 2x 3y 8 size 12{ left (2x - 3y right ) rSup { size 8{8} } } {} .

48384 x 5 y 3 size 12{ - "48384"x rSup { size 8{5} } y rSup { size 8{3} } } {}
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Find the coefficient of the a 5 b 4 size 12{a rSup { size 8{5} } b rSup { size 8{4} } } {} term in the expansion of a 2b 9 size 12{ left (a - 2b right ) rSup { size 8{9} } } {} .

2016 a 5 b 4 size 12{"2016"a rSup { size 8{5} } b rSup { size 8{4} } } {}
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Questions & Answers

anyone know any internet site where one can find nanotechnology papers?
Damian Reply
research.net
kanaga
Introduction about quantum dots in nanotechnology
Praveena Reply
what does nano mean?
Anassong Reply
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?
Damian Reply
absolutely yes
Daniel
how to know photocatalytic properties of tio2 nanoparticles...what to do now
Akash Reply
it is a goid question and i want to know the answer as well
Maciej
characteristics of micro business
Abigail
for teaching engĺish at school how nano technology help us
Anassong
Do somebody tell me a best nano engineering book for beginners?
s. Reply
there is no specific books for beginners but there is book called principle of nanotechnology
NANO
what is fullerene does it is used to make bukky balls
Devang Reply
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
Abhijith Reply
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
so some one know about replacing silicon atom with phosphorous in semiconductors device?
s. Reply
Yeah, it is a pain to say the least. You basically have to heat the substarte up to around 1000 degrees celcius then pass phosphene gas over top of it, which is explosive and toxic by the way, under very low pressure.
Harper
Do you know which machine is used to that process?
s.
how to fabricate graphene ink ?
SUYASH Reply
for screen printed electrodes ?
SUYASH
What is lattice structure?
s. Reply
of graphene you mean?
Ebrahim
or in general
Ebrahim
in general
s.
Graphene has a hexagonal structure
tahir
On having this app for quite a bit time, Haven't realised there's a chat room in it.
Cied
what is biological synthesis of nanoparticles
Sanket Reply
what's the easiest and fastest way to the synthesize AgNP?
Damian Reply
China
Cied
types of nano material
abeetha Reply
I start with an easy one. carbon nanotubes woven into a long filament like a string
Porter
many many of nanotubes
Porter
what is the k.e before it land
Yasmin
what is the function of carbon nanotubes?
Cesar
I'm interested in nanotube
Uday
what is nanomaterials​ and their applications of sensors.
Ramkumar Reply
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
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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?
William Reply
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?
Chine Reply
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?
Chalton Reply

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Source:  OpenStax, Applied finite mathematics. OpenStax CNX. Jul 16, 2011 Download for free at http://cnx.org/content/col10613/1.5
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