# 0.11 Sets and counting: homework  (Page 3/5)

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In how many different ways can five people be seated in a row if two of them insist on not sitting next to each other?

In how many ways can 3 English, 3 history, and 2 math books be set on a shelf, if the English books are set on the left, history books in the middle, and math books on the right?

72

In how many ways can 3 English, 3 history, and 2 math books be set on a shelf, if they are grouped by subject?

You have 5 math books and 6 history books to put on a shelf with five slots. In how many ways can you put the books on the shelf if the first two slots are to be filled with math books and the next three with history books?

2,400

You have 5 math books and 6 history books to put on a shelf with five slots. In how many ways can you put the books on the shelf if the first two slots are to be filled with the books of one subject and the next three slots are to be filled with the books of the other subject?

## Circular permutations and permutations with similar elements

Do the following problems using the techniques learned in this section.

In how many different ways can five children hold hands to play "Ring Around the Rosy"?

24

In how many ways can three people be made to sit at a round table?

In how many different ways can six children ride a "Merry Go Around" with six horses?

120

In how many ways can three couples be seated at a round table, so that men and women sit alternately?

In how many ways can six trinkets be arranged on a chain?

120

In how many ways can five keys be put on a key ring?

Find the number of different permutations of the letters of the word MASSACHUSETTS.

64,864,800

Find the number of different permutations of the letters of the word MATHEMATICS.

Seven flags, three red, two white, and two blue, are to be flown on seven poles. How many different arrangements are possible?

210

How many different ways can three pennies, two nickels and five dimes be arranged in a row?

How many four-digit numbers can be made using two 2's and two 3's?

6

How many five-digit numbers can be made using two 6's and three 7's?

If a coin is tossed 5 times, how many different outcomes of 3 heads, and 2 tails are possible?

10

If a coin is tossed 10 times, how many different outcomes of 7 heads, and 3 tails are possible?

If a team plays ten games, how many different outcomes of 6 wins, and 4 losses are possible?

210

If a team plays ten games, how many different ways can the team have a winning season?

## Combinations

Do the following problems using combinations.

How many different 3-people committees can be chosen from ten people?

120

How many different 5-player teams can be chosen from eight players?

In how many ways can a person choose to vote for three out of five candidates on a ballot for a school board election?

10

Compute the following:

1. $9C2$

2. $6C4$

3. $8C3$

4. $7C4$

How many 5-card hands can be chosen from a deck of cards?

2,598,960

How many 13-card bridge hands can be chosen from a deck of cards?

There are twelve people at a party. If they all shake hands, how many different hand-shakes are there?

66

In how many ways can a student choose to do four questions out of five on a test?

what is the stm
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 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
Difference between extinct and extici spicies
While the American heart association suggests that meditation might be used in conjunction with more traditional treatments as a way to manage hypertension
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?