# 0.11 Sets and counting: homework  (Page 4/5)

 Page 4 / 5

Five points lie on a circle. How many chords can be drawn through them?

10

How many diagonals does a hexagon have?

There are five teams in a league. How many games are played if every team plays each other twice?

20

A team plays 15 games a season. In how many ways can it have 8 wins and 7 losses?

In how many different ways can a 4-child family have 2 boys and 2 girls?

6

A coin is tossed five times. In how many ways can it fall three heads and two tails?

The shopping area of a town is a square that is six blocks by six blocks. How many different routes can a taxi driver take to go from one corner of the shopping area to the opposite cater-corner?

924

If the shopping area in [link] has a rectangular form of 5 blocks by 3 blocks, then how many different routes can a taxi driver take to drive from one end of the shopping area to the opposite kitty corner end?

## Combinations involving several sets

Following problems involve combinations from several different sets.

How many 5-people committees consisting of three boys and two girls can be chosen from a group of four boys and four girls?

24

A club has 4 men, 5 women, 8 boys and 10 girls as members. In how many ways can a group of 2 men, 3 women, 4 boys and 4 girls be chosen?

How many 4-people committees chosen from four men and six women will have at least three men?

25

A batch contains 10 transistors of which three are defective. If three are chosen, in how many ways can one get two defective?

In how many ways can five counters labeled A, B, C, D and E at a store be staffed by two men and three women chosen from a group of four men and six women?

14,400

How many 4-letter word sequences consisting of two vowels and two consonants can be made from the letters of the word PHOENIX if no letter is repeated?

Three marbles are chosen from an urn that contains 5 red, 4 white, and 3 blue marbles. How many samples of the following type are possible?

All three white.

4

Two blue and one white.

One of each color.

60

All three of the same color.

At least two red.

80

None red.

Five coins are chosen from a bag that contains 4 dimes, 5 nickels, and 6 pennies. How many samples of five of the following type are possible?

At least four nickels.

51

No pennies.

Five of a kind.

7

Four of a kind.

Two of one kind and two of another kind.

1,410

Three of one kind and two of another kind.

Find the number of different ways to draw a 5-card hand from a deck to have the following combinations.

Three face cards.

171,600

A heart flush(all hearts).

Two hearts and three diamonds.

22,308

Two cards of one suit, and three of another suit.

Two kings and three queens.

24

Two cards of one value and three of another value.

## Binomial theorem

Use the Binomial Theorem to do the following problems.

Expand ${\left(a+b\right)}^{5}$ .

${a}^{5}+{5a}^{4}b+\text{10}{a}^{3}{b}^{2}+\text{10}{a}^{2}{b}^{3}+5{\text{ab}}^{4}+{b}^{5}$

Expand ${\left(a-b\right)}^{6}$ .

Expand ${\left(x-2y\right)}^{5}$ .

${x}^{5}-\text{10}{x}^{4}y+\text{40}{x}^{3}{y}^{2}-\text{80}{x}^{2}{y}^{3}+\text{80}{\text{xy}}^{4}-\text{32}{y}^{5}$

Expand ${\left(2x-3y\right)}^{4}$ .

Find the third term of ${\left(2x-3y\right)}^{6}$ .

$\text{2160}{x}^{4}{y}^{2}$

Find the sixth term of ${\left(5x+y\right)}^{8}$ .

Find the coefficient of the ${x}^{3}{y}^{4}$ term in the expansion of ${\left(2x+y\right)}^{7}$ .

280

Find the coefficient of the ${a}^{4}{b}^{6}$ term in the expansion of ${\left(3a-b\right)}^{\text{10}}$ .

A coin is tossed 5 times, in how many ways is it possible to get three heads and two tails?

10

#### Questions & Answers

Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
what king of growth are you checking .?
Renato
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
Stoney Reply
why we need to study biomolecules, molecular biology in nanotechnology?
Adin Reply
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
Adin
why?
Adin
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?
Damian Reply
research.net
kanaga
sciencedirect big data base
Ernesto
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
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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