# 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

how do you translate this in Algebraic Expressions
linda Reply
Need to simplify the expresin. 3/7 (x+y)-1/7 (x-1)=
Crystal Reply
. After 3 months on a diet, Lisa had lost 12% of her original weight. She lost 21 pounds. What was Lisa's original weight?
Chris 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
what is nano technology
Sravani Reply
what is system testing?
AMJAD
preparation of nanomaterial
Victor Reply
Yes, Nanotechnology has a very fast field of applications and their is always something new to do with it...
Himanshu Reply
good afternoon madam
AMJAD
what is system testing
AMJAD
what is the application of nanotechnology?
Stotaw
In this morden time nanotechnology used in many field . 1-Electronics-manufacturad IC ,RAM,MRAM,solar panel etc 2-Helth and Medical-Nanomedicine,Drug Dilivery for cancer treatment etc 3- Atomobile -MEMS, Coating on car etc. and may other field for details you can check at Google
Azam
anybody can imagine what will be happen after 100 years from now in nano tech world
Prasenjit
after 100 year this will be not nanotechnology maybe this technology name will be change . maybe aftet 100 year . we work on electron lable practically about its properties and behaviour by the different instruments
Azam
name doesn't matter , whatever it will be change... I'm taking about effect on circumstances of the microscopic world
Prasenjit
how hard could it be to apply nanotechnology against viral infections such HIV or Ebola?
Damian
silver nanoparticles could handle the job?
Damian
not now but maybe in future only AgNP maybe any other nanomaterials
Azam
Hello
Uday
I'm interested in Nanotube
Uday
this technology will not going on for the long time , so I'm thinking about femtotechnology 10^-15
Prasenjit
can nanotechnology change the direction of the face of the world
Prasenjit Reply
At high concentrations (>0.01 M), the relation between absorptivity coefficient and absorbance is no longer linear. This is due to the electrostatic interactions between the quantum dots in close proximity. If the concentration of the solution is high, another effect that is seen is the scattering of light from the large number of quantum dots. This assumption only works at low concentrations of the analyte. Presence of stray light.
Ali Reply
the Beer law works very well for dilute solutions but fails for very high concentrations. why?
bamidele Reply
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
Privacy Information Security Software Version 1.1a
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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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 By By Mistry Bhavesh