# 0.11 Sets and counting: homework  (Page 2/5)

 Page 2 / 5

In a city election, there are 2 candidates for mayor, and 3 for supervisor. Use a tree diagram to find the number of ways to fill the two offices.

There are 4 roads from Town A to Town B, 2 roads from Town B to Town C. Use a tree diagram to find the number of ways one can travel from Town A to Town C.

8

Brown Home Construction offers a selection of 3 floor plans, 2 roof types, and 2 exterior wall types. Use a tree diagram to determine the number of possible homes available.

For lunch, a small restaurant offers 2 types of soups, three kinds of sandwiches, and two types of soft drinks. Use a tree diagram to determine the number of possible meals consisting of a soup, sandwich, and a soft drink.

12

A California license plate consists of a number from 1 to 5, then three letters followed by three digits. How many such plates are possible?

A license plate consists of three letters followed by three digits. How many license plates are possible if no letter may be repeated?

15,600,000

How many different 4-letter radio station call letters can be made if the first letter must be K or W and none of the letters may be repeated?

How many seven-digit telephone numbers are possible if the first two digits cannot be ones or zeros?

6,400,000

How many 3-letter word sequences can be formed using the letters $\left\{a,b,c,d\right\}$ if no letter is to be repeated?

A family has two children, use a tree diagram to determine all four possibilities.

BB, BG, GB, GG

A coin is tossed three times and the sequence of heads and tails is recorded. Use a tree diagram to determine the different possibilities.

In how many ways can a 4-question true-false test be answered?

16

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

A combination lock is opened by first turning to the left, then to the right, and then to the left again. If there are 30 digits on the dial, how many possible combinations are there?

27,000

How many different answers are possible for a multiple-choice test with 10 questions and five possible answers for each question?

## Permutations

Do the following problems using permutations.

How many three-letter words can be made using the letters $\left\{a,b,c,d,e\right\}$ if no repetitions are allowed?

60

A grocery store has five checkout counters, and seven clerks. How many different ways can the clerks be assigned to the counters?

A group of fifteen people who are members of an investment club wish to choose a president, and a secretary. How many different ways can this be done?

210

Compute the following.

1. $9P2$

2. $6P4$

3. $8P3$

4. $7P4$

In how many ways can the letters of the word CUPERTINO be arranged if each letter is used only once in each arrangement?

362,880

How many permutations of the letters of the word PROBLEM end in a vowel?

How many permutations of the letters of the word SECURITY end in a consonant?

25,200

How many permutations of the letters PRODUCT have consonants in the second and third positions?

How many three-digit numbers are there?

900

How many three-digit odd numbers are there?

In how many different ways can five people be seated in a row if two of them insist on sitting next to each other?

48

#### 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
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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