Ans. Total xxxxxxxx Students xxxx have xxxxx maths x m xxxxxxxx that xxxx taken xxxxxxx of xxxxx P x Students xxxx have xxxxx both x m x Students xxxx have xxxxx only xxxxx - xxxxxxxx that xxxx taken xxxx... ....... Total xxxxxxxx Students xxxx have xxxxx maths x m xxxxxxxx that xxxx taken xxxxxxx of xxxxx P x Students xxxx have xxxxx both x m x Students xxxx have xxxxx only xxxxx - xxxxxxxx that xxxx taken xxxx history xx maths x a xxxxxxxx that xxxx taken xxxxxx math xx history x mUh x m x h xx m x - x Students xxxx have xxxxx only xxxxx - x Students xxxx have xxxx one xx discreet xxxx or xxxxxxx of xxxx P xxxx discrete xxxx P xxxx history xx math x Students xxxx neither xx course x mUh x a xxxxx of xxxxx option xxxxx wheat xxxxx and xxxxxx free x e x number xx of xxxxxxxxx sizes xxx whole xxxxx no xx different xxxxx for xxxxx crust xx of xxxxxxxxx sizes xxx glunten xxxxx therefore xx of xxxxxxxxx crust xxxxxx taking xxxx into xxxxxxxxxxxxx b xxxxxxxxx size xxx whole xxxxx Available xxxx for xxxxx crust xxxxxxxxx size xxx gluten xxxx crust xxx different xxxxx of xxxxxx toppings xx of xxxx of xxxxxxxxx a xxxxx from x Now xxx each xx choices xx have xxxxx of xxxxx toppings xxxxxxxxx no xx different xxxxxx customer xxx c xxxx topping xxx topping xxxxx no xx topping xxx Choosing xxxxxxxx topping xxxx can xx done xx C xxxx C x n xx of xxxx of xxxxxxxx n xxxxxxxx item xxxx m xxxxxxxxx items x No xx veg xxxxxxx now xx of xxxx of xxxxxxxx distinct xxx toppings xxxx is x ways x total xxxxxxx in xxx range xx including xxxx Numbers xxxxxxxxxx all xxx four xxxxxx same xx no xx digits xxx containing xxx digits xxxxxxx - x Every xxxxxxxx combination xx three xxxxxxx digits xx this xxxxx can xxx with xx five xxxxxxxx even xxxxx digits xx or xxxx possible xxx final xxxxxx so xxxxx are xxxx as xxxx ending xxxx odd xxxxxx as xxxx even xxxx Thus xxxxxxx half xxx numbers xx the xxxxx end xxxx an xxx digit x There xxx possible xxx final xxxxxx For xxxx of xxxxx there xxx possible xxxxx digits xxx other xxxx odd xxxxxxx plus xxx For xxxx possible xxxxxxxxxxx of xxxx and xxxxx digit xxxxx are xxxxxxxx choices xxx each xx the xxxxxx digits xxx we xxx t xxxxxx the xxxx digit xxx both xx there xxx only xxxxxxx for xxx pair xx middle xxxxxx Thus xxxxx are xxxxxxx in xxxx range xxxx end xxxx an xxx digit xxx have xx repeated xxxxxx d xxxxx are xxxxxxxx digit xxxxxxxxx for xxx non- xxxxx If xxx first xxxxx isn x a xxxxx are xxxx other xxxxxxxxxxxxx for xx because xx can x be xxxx or xx the xxxx digit xxx t xxxxx possibilities xxxxx are xxxxx possibilities xxx it xx there xxx numbers xx this xxxxx with xxxxxxx digits xxxx are x a xx of xxxxxxx in xxxxxxx alphabet x Size xx password xxxx letter xx the xxxxxxxx can xx selected xx ways xxxxxxxxx no xx different xxxxxxxx passwords x taking xxxx the xxxxx into xxxxxxxxxxxxx sample xxxxx becomes x e xxxxx case xxx upper xxxx alphabets xx no xx ways xx selecting xxxx letter xx password xxxxx password xxx letters xxxxx possible xxxxxxxxx c x tal xxxxxxxxxx in xxxxxxxx first xxxxxxxxxx are xxxxxxxxxx No xx ways xx choosing xxxx Now xxxx character xx digit xx of xxxxxx Therefore xxxxxxxx passwords xxxx use x combination xx upper- xxx lower-case xxxxxxxxxx as xxxx as xxxxxxx one xxxxxxx digit xx the xxxx position x numeric xxxxx can xxxxxx of xxxxxx i x in xxxx so xxxxxxxx passwords xxxx use x combination xx upper- xxx lower-case xxxxxxxxxx as xxxx as xxxxxxx one xxxxxxx digit xx the xxxxxxxx of xxx numeric xxxxx is xxxxxxxx a xxx logic xx very xxxxxx since xx have xxxx letters xx English xxxxxxxxx and xxxxx are xxxxxxxx so xxxxxxx students xxxxx same xxxx initials x according xx the xxxxxxxx if xxx bus xxxxxxxxxx students xxx number xx student xxxx can xx carried xx bus xxxx a xxxxxxxxxx of xxxxxxxx So xxxxx is xxx buses xxxx or xxxx students xx arrange x distinct xxxxxxx from x distinct xxxxxxx the xxxxxxx is xxxxx by xxx lt x lt x where xxx n xxx and xxxxx n x n- xx x x x xx for xxxxxxxxx different xxxxxxx from xxxx of xx given xx P x which xxxxxxx to x x xxxx This xxxxxxxx is xxxxxxx to xxx here xxxx we xxx the xxxxxxxxxxx formula xxx permuting xxxxxx out xx the xxxxxx is xxxxx by x P x to xxxxxxxxxxx figures x Three xxxx student xxx two xxxxxxxx students xx condition xx given xx the xxxxxxxx so xxxx of xxx boy xxx occupy xxx of xxxxxxxxx One xxx can xxxxxx any xx position xx next xxx can xxxxxx the xxxxxxxxx position xxxxxxxxx the xxxxx boy xxx occupy xxx remaining xxxxxxxx and xx on xxxxxxxxx math xxx comp xxxxxxx can xxxxx the xxxxx in xxxx b xxx st xxxxxxxx we xxxx a xxxxxxxx student xx per xxx question xxxxx st xxxxxxxx can xx occupied xx choosing xxx of xxxxxxxx students xxxx turned xxxx This xxx be xxxx in x ways xxx the xxxxxxxxx position xxx be xxxxxxxx in xxxx ways xx of xxxx in xxxxx student xxx enter xx computer xxxxxxx has xx st xxxx Choosing xxxxxxxx from x set xx can xx done xx C xxxx subset xxxx Odd xx elements xxx if xxx of xxxxxxx with xxxxxxxx Now xx of xxxx of xxxxxxxx - xxxxxxx C xxxxxxx C xxxxxxxx C xxxxxxxx C xxxxxxxx C xxxxx Now xxxxx ways xx subset xxxx odd xxxxx ways x At xxxx element xxxxx that xxxx set xxx contain xxxxxxxx For x subset xxxx element xxxxxxxx no xx set xxx a xxxxxx with xxxxxxxx possible xx of xxxxxxxx i x st xxxxxxx can xx chosen xx ways xx element xxx be xxxxxx in xxxx and xxxx can xx arranged xx Ways xxx A xxxxxx with xxxxxxxx no xx possible xxxxxxx So xxxxx ways xx forming xxxxxx with xxxxxx element xxxxxx space xxx unbiased xxxx outcomes x probality xx an xxxxx is xxxxx by xxxxxxxx outcome xxxxxxx by xxx sample xxxxx P x Probable xxxxxxx sample xxxxx Probablity xxxx the xx that xxxxxxx when x dice xx rolled x are xx i x divisible xx i x cases xxx of xx the xxxxxxxxx of x no xxxx appears x dice xxx is xxxxxxxxx by x Possible xxxx that xxx sum xx no xx greater xxxx or xxxxx to xx dice xx tossed xxxxx cases xxx sum xxxxx ways xxx equal xxxx sum xxxxx ways xxx equal xxx Total xxxxxxxx case xxx a xxxxx of xxxx and xxx atleast xxxx Sample xxxxx for xxx throw xx two xxxxx as xxxx the xxxx can xxxx possible xxxxxxxx respectively xxxxxxxxx probability xxx dices xxxxxx sum xx atleast x total xxxxxxxxx in xxxx No xx members xx committee xxx no xx ways xx choosing xxxxxxx from x a xxx a xxxx coin xxxxxxxx outcome xxxx or xxxx Probability xx getting x head xxxxxxxxxx of xxxxxxx a xxxx All xxxxxxxx outcomes xxx tossing xxx coin xxxx are xxxx HHHT xxxx HTHH xxxx HHTT xxxx HTTH xxxx THHT xxxx HTTT xxxx TTHT xxxx TTTT xx we xxxx total xx possible xxxxxxxx b xxxxxxxxxxx of xxxxxxxxx all xxxx head xxxx ques x c xxxxxxxxxxx of xxxxxxxxx two xxxx and xxx tail xxxx rd xxxx of xxxx a x Probability xx no xxxx Probability xx all xxxx from xxxx ques x e xxxxxxxxxxx of xxxxxxx at xxxxx head xxxxxxxxxxx of xxxxxxx head xxxxxxxx ways xx getting xxxx ways xxxx ways xxxx ways xxxx way xx probability xx getting xx least xxxx a xxx bag xxxxxxxx blue xxxxx white xxx red xxxxxxx Total xxxxxxx marbles xx of xxxx of xxxxxxx blue xxxxxx Therefore xxxxxxxxxxx f xxxxxxx blue xxxxxx in xx attempt xxx after x draw xx replacement xx done xxxxxx space xxxxxxx the xxxx so xxxxxxxx of xxxxxxx blue xxxx in xxxxxx draw xx also xx combined xxxxxxxxxxx of xxxx marble xx st xxx nd xxxxxxx b xxxxx marbles xxxxxxx No xx ways xx getting xxxx marble xxxxxxxxx probability x getting xxxx marble xx st xxxxxxx Replacement xx done xx the xxxxxx space xxxxxxx the xxxx No xx ways xx selecting x non xxxx marble x So xxxxxxxxxxx of xxxxxxxxx a xxx blue xxxxxx is xxx using xxxxxxxx probability xxx a xxxx ball xx st xxxxxxx and x non xxxx ball xx second xxxxxxx is xxxxx by x question xxx clear xx no xx selections xxx mentioned x Total xxxxxxx marbles xx of xxxx of xxxxxxx blue xxxxxx Therefore xxxxxxxxxxx f xxxxxxx blue xxxxxx in xx attempt xxx after x draw xx replacement xx not xxxx So xx of xxxx balls xxxxxx Sample xxxxx becomes xxx the xxxxxxxxxxx of xxxxxxx blue xxxx in xxxxxx draw xx combined xxxxxxxxxxx of xxxx marble xx st xxx nd xxxxxxx when xxxxxxxxxxx is xxx done xxxxx newcomers xx club xx of xxxxxxx in xxxxxxxxx Now xx of xxxx of xxxxxxxx members xxxx C xxx problem xx a xxxx no xx days xx in x group xx members xxx people xxx have xxxxxxxxx days xx birth xx the xx person xxxxxxxxxxx shares xxx birthday xxxx some xxxxx person Read More

Ans. Initial xxxx Linear xxxxxxxxxxx has xxxxxxx use xx businesses xx it xxxxxx solutions xx real xxxx situations xxx example xx has xxxx used xx the xxxxxxxxx like xxxxxxx for xxxxx optimally xxxxx space... ....... Initial xxxx Linear xxxxxxxxxxx has xxxxxxx use xx businesses xx it xxxxxx solutions xx real xxxx situations xxx example xx has xxxx used xx the xxxxxxxxx like xxxxxxx for xxxxx optimally xxxxx space xx their xxxxxx Any xxxxxx store xxx limited xxxxx and xxxxxxxxx have xxxxxxx time xx shop xx a xxxxx therefore xxxxxxxxx tend xx optimize xxxxx shelf xxxxx for xxxxxxxxxx visibility xx the xxxxxxxx It xxx been xxxxxxx that xxx middle xxxxx often xxxxxxxx the xxxx item xx opposed xx other xxxxx and xxxx reflect xxx use xx optimization xx a xxxxxxxxx context xx Walmart xx is xxxx to xxxxxxxx the xxxxxxxxx shelf xxxxx For xxxxxxxx there xxx products xxx spaces xx shelf xxxxxx Decision xxxxxxxx It xx Xij xxxxxx of xxxxxxxx i xxx on xxxxx j xxxxxxxxxxx These xxx as xxxxxxxx Number xx products xx each xxxx allocated xx a xxxxxx it xxxxxxx that xxxxxxxxxxxxxx the xxxxxxxx in xxx store xxx entire xxxxxx of xxxxxxxx i xxx on xxx shelf x must xx equal xx the xxxxxxx quantity xx the xxxxxxxx i xxxx are xxxxxx in xxx retail xxxxx Maximum xxxxxx of xxxxxxxx that xxx be xxxxxxxx on xxx shelf- xx means xxxx the xxxxx number xx products x that xxx sorted xx shelf x must xxx exceed xxx maximum xxxxxxx capacity xxxxxxx number xx products- xx means xxx total xxxxxx of xxxxxxxx i xxxx must xx put xxxx on xxxxx j xxxx be x positive xxxxxxx equal xx greater xxxx zero xxxxxxxxx function xxx objective xxxxxxxx has xxxxx sums xxx first xx finds xxx cost xx assigning xxx product xx shelf xx determines xxx the xxxxxxxx must xx arranged xxxxx the xxxxxxx for xxxxxxxxxx time xx also xxxxxxx that xxx products xxxx low xxxxx rotation xxx placed xx the xxxx shelf xxxxx The xxxxxx and xxxxx terms xxxx the xxx types xx pairwise xxxxxxxxx among xxx products xxxxxxxx There xxx benefits xxxxx the xxxxxxx derives xx using xxx technique xx allows xxx minimizing xxxx and xxxx of xxxxxxxxxx products xx the xxxxxxx It xxxxxx for xxxxxx visibility xx the xxxxxxxx on xxx shelves xxx hence xxxxxx management xx the xxxxxxxx is xxxx Lessons xxxxxx Major xxxxxxx have xxxx learnt xxxx this xxxxxxxxx situation xx helped xx understanding xxx use xx LPP xxxxxxxxxxxx technique xx solving xxx problem xx shelf xxxxx utilization xx helps xx comprehending xxx concept xx optimization xx an xxxxxxxxx manner xxxxxxxxx Kalkas x Simplified xxxxx Problem xx a xxxxxx Linear xxxxxxx Programming xxxxxxx Retrieved xxxx https xxxxxxxx aalto xx bitstream xxxxxx master xxxxxx Sami xxx sequence Read More

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Ans. In xxxx course x employ x self-management xxxxxx to xxxx on xxxx To xxxxx I xxxx outlined xxx goals xxx objectives x wish xx accomplish x put xxxx in xxxxxxx to xxxxx back xx them xxxxx and xxxxxx I'm... ....... In xxxx course x employ x self-management xxxxxx to xxxx on xxxx To xxxxx I xxxx outlined xxx goals xxx objectives x wish xx accomplish x put xxxx in xxxxxxx to xxxxx back xx them xxxxx and xxxxxx I'm xx the xxxxx track x also xxxxxx my xxxxx into xxxxxxx easier-to-achieve xxxxxx keeping xx on xxxxx and xxxx being xxxxxxxx I xxxx to x schedule xxx set xxxxx particular xxxxx periods xx study x also xxx a xxxxxxxx to xxxxxxx study xxxxxxxx and xxxxx necessary xxxxxx so xxxx I xxx plan x use x timer xx be xxxxxxxx and xxxxxxx my xxxx and x reward xxxxxx as x finish xxxxx I xxxx take xxxxxxx breaks xx refresh xxx sustain xx motivation xxxx technique xxxxxxx that x am xxxxxx closer xx my xxxxxxxxxx and xxxxx me xxxx motivated xxx focused xx also xxxxx me xx stay xxxxxxxxx with xxx course xxx my xxxxx and xxxxx me xxxx feeling xxxxxxxxxxx or xxxxxx out Read More

Ans. Hearing xxx word xxxx can xx very xxxxxxxxx for xxxxxxxxx people xxxx can xx very xxxxxxx to xxxxx the xxxx long xxxxxx game xxxxx the xxxxx starts xxxxxxx at xxxxxx the xxxxx for xxxx The xxxxxxx its... ....... Hearing xxx word xxxx can xx very xxxxxxxxx for xxxxxxxxx people xxxx can xx very xxxxxxx to xxxxx the xxxx long xxxxxx game xxxxx the xxxxx starts xxxxxxx at xxxxxx the xxxxx for xxxx The xxxxxxx itself xxx make xxxxxx nervous xx it xx demanding xx nature xxx the xxxxxxxx to xxxxx problem xxx only x single xxxxxxxx A xxxxxxx can xxxxx the xxxxxx in xxx correct xxxxxx The xxxx for xxxxxxx around xxx bush xxxxxx the xxxxx becomes xxxx and xxxx some xxxxxxxxx anxiety xxx stress xxxxxxxx Some xxxxxxxx causes xx anxiety xxx be xxx unpleasant xxxxxxxxxx with xxx subject xxx standard xx fellow xxxxxx in xxx class xxxxx tests xxx exams xxxx of xxxxxx embarrassment xxx fear xx showing xxx result xx the xxxxxxx Some xxxxxxxxxx measures xxxx can xx done xx lower xxx anxiety xxx first xx acknowledge xxxx there xx anxiety xxxx being xxxxxxxx for xxx subject xxxxxxxxxx and xxxxxxx some xxxxxxxx in xxx subject xxxxxxx which xxx be xxxx by xxxxxxxxxxx a xxxxxx mindset xxxxx attentive xx class xxx preparing xxx the xxxx can xx some xxxxxxxxxx for xxxxxxxxxx stress Read More