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

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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

are nano particles real
yeah
Joseph
Hello, if I study Physics teacher in bachelor, can I study Nanotechnology in master?
no can't
Lohitha
where we get a research paper on Nano chemistry....?
nanopartical of organic/inorganic / physical chemistry , pdf / thesis / review
Ali
what are the products of Nano chemistry?
There are lots of products of nano chemistry... Like nano coatings.....carbon fiber.. And lots of others..
learn
Even nanotechnology is pretty much all about chemistry... Its the chemistry on quantum or atomic level
learn
da
no nanotechnology is also a part of physics and maths it requires angle formulas and some pressure regarding concepts
Bhagvanji
hey
Giriraj
Preparation and Applications of Nanomaterial for Drug Delivery
revolt
da
Application of nanotechnology in medicine
has a lot of application modern world
Kamaluddeen
yes
narayan
what is variations in raman spectra for nanomaterials
ya I also want to know the raman spectra
Bhagvanji
I only see partial conversation and what's the question here!
what about nanotechnology for water purification
please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
Damian
yes that's correct
Professor
I think
Professor
Nasa has use it in the 60's, copper as water purification in the moon travel.
Alexandre
nanocopper obvius
Alexandre
what is the stm
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
Rafiq
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
Damian
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
how nano science is used for hydrophobicity
Santosh
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
Rafiq
what is differents between GO and RGO?
Mahi
what is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.? How this robot is carried to required site of body cell.? what will be the carrier material and how can be detected that correct delivery of drug is done Rafiq
Rafiq
if virus is killing to make ARTIFICIAL DNA OF GRAPHENE FOR KILLED THE VIRUS .THIS IS OUR ASSUMPTION
Anam
analytical skills graphene is prepared to kill any type viruses .
Anam
Any one who tell me about Preparation and application of Nanomaterial for drug Delivery
Hafiz
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
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?