SOLVEEACHOFTHEFOLLOWINGPROBLEMS:

1.SUPPOSEA BUSINESSOWNERHAS A CHOICE OF FIVELOCATIONS IN WHICH TO ESTABLISHHER BUSINESS .SHE DECIDES TO RANK EACH LOCATION ACCORDING TO CERTAIN CRITERIA , SUCH AS PRICE OF THE STORE AND PARKINGFACILITIES . HOW MANYDIFFERENTWAYSCAN SHE RANKTHE FIVECITIES?

2.INHOWMANYWAYSCAN8INDIVIDUALSBESEATEDIN A ROUND TABLEWITH8CHAIRS ?

a )SUPPOSE2PERSONSWANTEDTO BESEATEDSIDE BY SIDE , IN HOW MANYWAYSCAN THEYDO IT?

B )IN HOWMANYWAYSCAN THESE8INDIVIDUALSARRANGETHEMSELVES IF

2AMONGTHEM REFUSETO SIT TOGETHER?

3.HOWMANYDIFFERENTSIGNALSUSING THREE DISTINCTFLAGS CANBEMADE IF THERE AREFIVE DIFFERENT FLAGSFROM WHICH TO SELECT ?

4.HOWMANY DISTINCTPERMUTATIONS CAN BEMADE FROM THELETTERS OF THEWORD:

A)PHILIPPINES

B)COMMISSION

C)BOOKKEEPING

D)ECONOMETRICS

5.HOWMANY DIFFERENT 4 - DIGIT NUMBERS CAN BEFORMED FROM THE DIGITS 2, 3 , 4 , 5 , 6 , 7 , AND8IF:

A)REPETITIONOF DIGITS ISNOT ALLOWED ?

B )REPETITION OFDIGITSISALLOWED ?

C)HOWMANYOFTHEM AREODD NUMBERS ?REFER TOLETTERA .

D )HOWMANYOFTHEM AREEVENNUMBERS?REFERTO LETTERB.

6.A COMMITTEEOF5 PEOPLE MUST BE SELECTED FROM 5 MENAND8WOMEN.HOWMANY WAYSCAN ASELECTION BE DONE IF THERE ARE AT LEAST 3WOMEN ON THE COMMITTEE .

7.AMANUFACTURER OFMAINFRAME COMPUTERS IS TRYING TO WIN A LARGE CONTRACT WITH HIS CLIENT . THE MANUFACTURER IS GOINGTO SEND TO THE CLIENT'SFACILITIES5SALESPERSONS, 7 TECHNICIANS , AND 3SOFTWARE ENGINEERS . IN HOWMANYWAYS CAN THESE 15 PEOPLE BE SELECTED IF THE MANUFACTURERS HAS AVAILABLE10 SALESPERSONS,9 TECHNICIANS , AND7SOFTWAREENGINEERS?

8.FROM 4 RED , 5 GREENAND 6BLACKBALLPENS,HOWMANYSELECTIONS OF9 BALLPENS AREPOSSIBLE IF 3OFEACHCOLOR ARE TO BESELECTED ?

9. IF A CARDIS DRAWNAT RANDOMFROM AN ORDINARYDECK OF 52CARDS , FIND THE PROBABILITY THAT ITIS:

A)ADIAMOND

B)AREDCARD

C)AHEARTORASPADE

D)NOTANACE

E)ABLACKCARDORAKING

10)SIXCOINS AREFLIPPED SIMULTANEOUSLY . WHAT ISTHEPROBABILITYTHAT

THERE ARE:

A)ATLEAST5HEADS ?

B)ATLEAST3TAILS?

C)NOHEAD?

D) ATMOST2TAILS?

11.IN AGRADUATING CLASS OF300 STUDENTS , 162STUDIED MATHEMATICS , 185 STUDIEDENGLISH, AND105STUDIED BOTHMATHEMATICS AND ENGLISH.IF ONEOF THESE STUDENTS ISSELECTED ATRANDOM FOR AN INTERVIEW

QUESTIONS: FIND THEPROBABILITY THAT:

A)THE STUDENT TAKES MATHEMATICSORENGLISH

B)THE STUDENT DOES NOT TAKE EITHER OF THESESUBJECTS

C.THESTUDENTTAKESMATHEMATICSBUTNOTENGLISH

12.IN ACERTAIN UNIVERSITY , 60 PERCENT OF ALL SOPHOMORES AREENROLLED IN MATHEMATICSCOURSE, 73 PER CENT AREENROLLEDIN AN ENGLISHCOURSEAND 49PER CENTARE TAKINGBOTH.A STUDENT ISRANDOMLYSELECTED FROMTHISUNIVERSITY.

A)WHATISTHEWPROBABILITY THATTHESTUDENT ISTAKINGAN ENGLISHCOURSE, IF ITISKNOWNTHAT HE/ SHE IS ENROLLEDIN AMATHEMATICSCOURSE ?

B)IF THESTUDENT IS TAKINGAN ENGLISHCOURSE , WHATISTHEPROBABILITY THATHE/ SHE ISALSOENROLLED IN AMATHEMATICSCOURSE?

13.THERCCOMPANYRENTSBUSESFROMAgencyxat26%OFTHE TIME , AGENCYY AT38% OF THE TIME , AND AGENCY ZAT THE REMAINDER OFTHETIME. IT IS KNOWNTHAT 10 % OF THEBUSES FROM AGENCYX , 20 %OFTHEBUSESFROMAGENCYY , AND5 % OF THEBUSESFROMAGENCYZHAVE DEFECTIVETIRES.IFABUSISRANDOMLYSELECTEDFROMACENTRALPOOLOFBUSES FROMTHESEAGENCIES, FINDTHEPROBABILITY THAT

A)THEBUSHASDEFECTIVETIRES

B)THE BUSISFROMAGENCYX, GIVENITHASDEFECTIVETIRES

C)THEBUSISFROMAGENCYZ, GIVENIT HASNON DEFECTIVETIRES .

14.ASUPERMARKETIN MARIKINA CITY OCCASIONALLYRECEIVESASHIPMENT OFLIVELOBSTERS .SEVENTY FIVEPERCENT OF THE TIME IS SPENT BY THE SUPERMARKET TO PLACEAN AD AND SELL OUT ITSSHIPMENT. ITALSO ADVERTISES THE AVAILABILITY OF THELOBSTER FOR80PERCENT OFTHESHIPMENTS .WHAT IS THEPROBABILITY THAT THE SUPERMARKETWILL SELL ANENTIRESHIPMENTIF IT ADVERTISES ?

15.TWO CARDS ARE DRAWN IN SUCCESSION FROM ADECK WITHOUTREPLACEMENT. WHAT ISTHEPROBABILITY THAT BOTH CARDS ARERED ? IF THE FIRST WILL BE RETURNED,WHAT IS THEPROBABILITY THATTHEFIRST CARDIS AN ACE AND THE SECOND IS A FACE CARD ?

16.APROFESSORIN A CERTAINCOLLEGE ISBEINGCONSIDERED FORPROMOTION AND ALSO FORTENURE .HEBELIEVES THEPROBABILITY THAT HEWILL OBTAIN TENURE IS0.80 AND THEPROBABILITY THAT HE WILL RECEIVEBOTHIS 0.60 .WHAT PROBABILITY DOESSHEASSIGNTO BEINGPROMOTED IFHEIS GRANTEDTENURE ?

17.A )HOWMANYWAYS CAN 10PASSENGERSBELINEDUPTOGETON ATRAIN?

B)IFACERTAIN 3PERSONS INSIST ON FOLLOWINGEACH OTHER, HOWMANYWAYSAREPOSSIBLE?

18.HOWMANYDIFFERENTTRIANGLESCAN BE FORMED USINGTHE VERTICESOFANOCTAGON?PENTAGON ?HEXAGON?

19.CLASSIFYTHEFOLLOWINGRANDOMVARIABLESASDISCRETEORCONTINUOUS

A.THE NUMBER OF UNITS OF SOMEPRODUCTSOLDON AGIVENDAY.

B.THE NUMBEROF CORRECTANSWERS IN A25 - ITEMQUESTION TEST

C.THE LENGTH OFTIMETOPLAY12HOLESOFGOLF

D.THE NUMBER OFEGGSLAIDEACHMONTH BY1HEN

E.THE LENGTHOFLIFE(INHOURS )OFALIGHTBULB

F.THENUMBEROFVEHICULARACCIDENTSEACH YEARINMETRO MANILA

G.THEWEIGHTOFGRAININ KILOGRAMSPRODUCEDPERHECTARE

20.MR.XISPLANNINGTO OPENABUSINESS. HISFRIEND TOLDHIMTHAT THEBUSINESSHAS A 3/5 PROBABILITY OFGAININGP 450,000 AND A2/5 PROBABILITY OF LOSING P 300,000.WHAT ISMR. X 'SEXPECTED VALUE FORHISBUSINESS ?WILL MR. XCONTINUEHISBUSINESS ?

Please answer the following problems with solutions and explanations

thank you so much for your help