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Permutation and CombinationQuestion and Answers: Page 23

Question Number 21799    Answers: 0   Comments: 2

There are n white and n red balls marked 1, 2, 3, ....n. The number of ways we can arrange these balls in a row so that neighbouring balls are of different colours is

Therearenwhiteandnredballsmarked1,2,3,....n.Thenumberofwayswecanarrangetheseballsinarowsothatneighbouringballsareofdifferentcoloursis

Question Number 21771    Answers: 0   Comments: 0

The result of 11 chess matches (as win, lose or draw) are to be forecast. Out of all possible forecasts, the number of ways in which 8 correct and 3 incorrect results can be forecast is

Theresultof11chessmatches(aswin,loseordraw)aretobeforecast.Outofallpossibleforecasts,thenumberofwaysinwhich8correctand3incorrectresultscanbeforecastis

Question Number 21768    Answers: 0   Comments: 2

Six cards and six envelopes are numbered 1, 2, 3, 4, 5, 6 and cards are to be placed in envelopes so that each envelope contains exactly one card and no card is placed in the envelope bearing the same number and moreover the card numbered 1 is always placed in envelope numbered 2. Then the number of ways it can be done is

Sixcardsandsixenvelopesarenumbered1,2,3,4,5,6andcardsaretobeplacedinenvelopessothateachenvelopecontainsexactlyonecardandnocardisplacedintheenvelopebearingthesamenumberandmoreoverthecardnumbered1isalwaysplacedinenvelopenumbered2.Thenthenumberofwaysitcanbedoneis

Question Number 21766    Answers: 1   Comments: 0

There are 3 apartments A, B and C for rent in a building. Each apartment will accept either 3 or 4 occupants. The number of ways of renting the apartments to 10 students

Thereare3apartmentsA,BandCforrentinabuilding.Eachapartmentwillaccepteither3or4occupants.Thenumberofwaysofrentingtheapartmentsto10students

Question Number 21760    Answers: 1   Comments: 0

There are m points on the line AB and n points on the line AC, excluding the point A. Triangles are formed joining these points (i) When point A is not included, (ii) When point A is included. The ratio of the number of such triangles is

TherearempointsonthelineABandnpointsonthelineAC,excludingthepointA.Trianglesareformedjoiningthesepoints(i)WhenpointAisnotincluded,(ii)WhenpointAisincluded.Theratioofthenumberofsuchtrianglesis

Question Number 21686    Answers: 0   Comments: 0

I have 6 friends and during a vacation I met them during several dinners. I found that I dined with all the 6 exactly on 1 day; with every 5 of them on 2 days; with every 4 of them on 3 days; with every 3 of them on 4 days; with every 2 of them on 5 days. Further every friend was present at 7 dinners and every friend was absent at 7 dinners. How many dinners did I have alone?

Ihave6friendsandduringavacationImetthemduringseveraldinners.IfoundthatIdinedwithallthe6exactlyon1day;withevery5ofthemon2days;withevery4ofthemon3days;withevery3ofthemon4days;withevery2ofthemon5days.Furthereveryfriendwaspresentat7dinnersandeveryfriendwasabsentat7dinners.HowmanydinnersdidIhavealone?

Question Number 21685    Answers: 0   Comments: 0

In a group of ten persons, each person is asked to write the sum of the ages of all the other 9 persons. If all the ten sums form the 9-element set {82, 83, 84, 85, 87, 90, 91, 92} find the individual ages of the persons (assuming them to be whole numbers of years).

Inagroupoftenpersons,eachpersonisaskedtowritethesumoftheagesofalltheother9persons.Ifallthetensumsformthe9−elementset{82,83,84,85,87,90,91,92}findtheindividualagesofthepersons(assumingthemtobewholenumbersofyears).

Question Number 21683    Answers: 1   Comments: 2

Suppose A_1 A_2 ...A_(20) is a 20-sided regular polygon. How many non-isosceles (scalene) triangles can be formed whose vertices are among the vertices of the polygon but whose sides are not the sides of the polygon?

SupposeA1A2...A20isa20−sidedregularpolygon.Howmanynon−isosceles(scalene)trianglescanbeformedwhoseverticesareamongtheverticesofthepolygonbutwhosesidesarenotthesidesofthepolygon?

Question Number 21651    Answers: 0   Comments: 4

How many four-digit numbers are there whose decimal notation contains not more than two distinct digits?

Howmanyfour−digitnumbersaretherewhosedecimalnotationcontainsnotmorethantwodistinctdigits?

Question Number 21693    Answers: 0   Comments: 15

How many six-digit numbers contain exactly four different digits?

Howmanysix−digitnumberscontainexactlyfourdifferentdigits?

Question Number 21598    Answers: 0   Comments: 0

Prove that ((n^2 !)/((n!)^n )) is an integer, n ∈ N.

Provethatn2!(n!)nisaninteger,n∈N.

Question Number 21587    Answers: 1   Comments: 1

If n objects are arranged in a row, then find the number of ways of selecting three of these objects so that no two of them are next to each other.

Ifnobjectsarearrangedinarow,thenfindthenumberofwaysofselectingthreeoftheseobjectssothatnotwoofthemarenexttoeachother.

Question Number 21572    Answers: 0   Comments: 0

Determine the largest 3-digit prime factor of the integer^(2000) C_(1000) .

Determinethelargest3−digitprimefactoroftheinteger2000C1000.

Question Number 21406    Answers: 0   Comments: 2

Find the number of ways in which n distinct balls can be put into three boxes so that no two boxes remain empty.

Findthenumberofwaysinwhichndistinctballscanbeputintothreeboxessothatnotwoboxesremainempty.

Question Number 21405    Answers: 1   Comments: 0

Four dice are rolled. The number of ways in which at least one die shows 3, is

Fourdicearerolled.Thenumberofwaysinwhichatleastonedieshows3,is

Question Number 21404    Answers: 1   Comments: 0

Prove that (6n)! is divisible by 2^(2n) .3^n .

Provethat(6n)!isdivisibleby22n.3n.

Question Number 21374    Answers: 0   Comments: 2

In how many ways can the letters of the word PATLIPUTRA be arranged, so that the relative order of vowels are consonants do not alter?

InhowmanywayscanthelettersofthewordPATLIPUTRAbearranged,sothattherelativeorderofvowelsareconsonantsdonotalter?

Question Number 20926    Answers: 0   Comments: 0

Question Number 17770    Answers: 1   Comments: 0

Find the number of ways the digits 0,1,2 and 3 can be permuted to give rise to a number greater than 2000.

Findthenumberofwaysthedigits0,1,2and3canbepermutedtogiverisetoanumbergreaterthan2000.

Question Number 16876    Answers: 1   Comments: 0

In how many ways can a family of 5 brothers be seated round a table if (i) 2 brothers must seat next to each other. (ii) 2 brothers must not seat together.

Inhowmanywayscanafamilyof5brothersbeseatedroundatableif(i)2brothersmustseatnexttoeachother.(ii)2brothersmustnotseattogether.

Question Number 16868    Answers: 1   Comments: 0

In how many ways can the letters of the word. EVERMORE be arrange if the word must begin with (i) R (ii) E

Inhowmanywayscanthelettersoftheword.EVERMOREbearrangeifthewordmustbeginwith(i)R(ii)E

Question Number 16836    Answers: 1   Comments: 0

Find how many number greater than 2,500 can be formed from the digit 0, 1, 2, 3, 4 if no digit can be used more than once.

Findhowmanynumbergreaterthan2,500canbeformedfromthedigit0,1,2,3,4ifnodigitcanbeusedmorethanonce.

Question Number 13508    Answers: 1   Comments: 0

5!! = ? please workings, how is the answer 15

5!!=?pleaseworkings,howistheanswer15

Question Number 12590    Answers: 0   Comments: 0

In a basic version of pocker , each players is dealth 5 cards from a standard 52 cards (no pocker). How many diferent 5 cards pocker hand are there ???

Inabasicversionofpocker,eachplayersisdealth5cardsfromastandard52cards(nopocker).Howmanydiferent5cardspockerhandarethere???

Question Number 12218    Answers: 1   Comments: 3

5!! = ?

5!!=?

Question Number 12087    Answers: 1   Comments: 0

In how many ways can 10 objects be split into two groups containing 4 and 6 objects respectively ?

Inhowmanywayscan10objectsbesplitintotwogroupscontaining4and6objectsrespectively?

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