2» a » a 9 5 PERMUTATIONS AND COMBINATIONS - PAST HSC QUESTIONS 1988-2006 ‘ett stpemnaeom se Qo) UR-Ie Find the tumber of six-leter arangements that can be made fom te leer inthe word SYDNEY. 360 Yr Supeentco tac Qu2)3US0e Letcach diferent srangement of all the loters of DELETED be called a word, i. Howsmany words are possible? In how many ofthese words will the 1 be separate!22 1) 420 it 300 ‘ett sUpemnaeon se Qs3) 305045 ‘There are tree idertical blue marbles and four identical yellow marbles arranged ina row. i. How many differen arrangements are posible? ji, Howsmany different arrangements of jus five ofthese marbles are posible? 35 i 25 ‘YrT superman se Qo) 3091 Containers ae coded by different arangements of coloured dots ina sow. The colours used ae red, ‘white, and blue. Inan arrangement, at most he ofthe dts ae red a mst wo of he dots ee white, and at most one is be. i. Find dhe mmber of different codes posibie if six dts are use. i, Onsome containers only five dots are used. Find the mmber of different codes posible inthis case, Justify your answers 60 ii 60 ‘elt stipenmeam he Qn) SU3-16 ‘Acass consists of 10 gies and 12 boys. How many ways are thereof selecting acommitee of 3 girls ‘and 2 boys from this class 7920 Yet spemteoo ve Qs) 3UR5-f0 Five travellers ave in @ town where there are five hotels. i. How many different aevommodaton arrangements ae there if here reno restrictions on where ‘the travellers stay? How many differen socommodstion rangement are there if each traveller tays aa diffrent hotel? ‘Suppose two ofthe travelers are husband and wife and must goto the same hotel. How many siferent accommodation arangements are there if he oer tee ean goto any ofthe other hater i) 3125 i 120 i) 320 ‘yr atpemseam ie Qn?) SUT “The figure show 9 points lying inthe plane, 5 of which ie on te line £. No other set of 3 ofthese points seolinear. How many sets of3 points ean be chosen from the 5 points lying on L? iow many differen triangles canbe formed using the 9 points as vertives?= pninrs ‘tb Upemcon ive On 309538 _ security lock has 8 bons labelled as shown ach person wg the Tok is given a3 fete code 1 ow anny diferent codes ae poste ifleterscan be epested an hi order importa? Ji, How many diffrent codes are posible eters canne be repeated and tc orders inportan? Ji, Now suppose tha tho lst pete by hong 5 batons down tgs tht order is NOT import. Hovr many diferent code are posite?1) 512 i) 330 3) 56 9) Yetturpemteom nse Qu9) sU96-14 ‘A.comitee of 3 men and 4 women ist be formed froma group of 8men and 6 women. Write an expression forthe mmber of ways this ean be done fy! 10) Ye1taupmtsomnse Qo 3199:28 “The staff in an office consists off males ond 7 females. How many committes of 5 staan be chosen ‘which contain exactly 3 femalesto | 20 1) Yett Supentcomse Qn) 3000-28 How many arangements of th letters of the word HOCKEYROO ate possible?® 50480 12) Yett su pemtcom se Qo) 3000-60 ‘A standard pack of 52 cards consists of 13 cards ofeach ofthe four suis: spades, hearts, clubs and diamonds. ic Inhow many ways ean six cards be selected without replacement so thet exactly two ae spades and four are clubs? (Assume tat the order of selection ofthe sx ead is nat important) Ji, Inhow many ways can sx cards be selected without replacement if atleast five must be ofthe same suit? (Assume that the order of selection ofthe six eards snot important Jo 58770 i 207636 13) Yeraupomseom ie Qat9) 3U0h-26 ‘The lena 4, £1, O and U are vowels. i, Howmany arangements of the letters inthe word ALGEBRAIC ae possible? ii, How many arangemens of the letters inthe wor ALGEBRAIC ae posible ifthe vowels must ‘occupy the 2nd, 3, Sth and Sth positions? 4) 182 440 i 1440 14) Yt 13UpemdeomtseQal) 300238 Seven people are to be seated at around table. i.” How many seating arrangement are possible? “Two people, Kevin and ill ese ost next to each other, How many seating arrangements ae then possble?= 1) 720 3) 480 15) Yer sUipernteom i Qos) 300338 How many nine-leter arrangements canbe made using Ietes of the word ISOSCELESS| 30240 16) Yet13uypemgcomse Quo 2003-40 A comite of 6s tobe chosen from /4 candidates. In how many different ways can this be dons? 3002 17) elt aUypemteom.ee Qu) 34063 ‘opie has five coloured blocks: ne red, one hve, one een, one yellow and one white. She stacks wo, tree, furor five blocks on tep of ane anether to form vertical tower. i, How many different towers ae there that she could form that are three blocks high? ji, low many different towers can she form in ttal2s 60 iy s20 Brora]Son a0 Biss bone Des yi ws pata 36 ws ieee, 91820 9 re Baa to 320th co one