Partial preview of the text
Download Permutations And Combinations JEE ADV Notes (Zero → Advanced) and more Study notes Mathematics in PDF only on Docsity!
aval numbers Be Factonio : The vonbnors procluct of nt natural o F ft iA fackorick ‘W (wen): bows rel by vl ow le Tale nu Wart) x Ca-rde- Zxr*X) foagyst Sapeanper 7 de axrercsk oot) (EY (ean (ay ore wrdnpinned BD) od am wu yekro 2) 1 trun jpode (4 EN) 21 (n-2)1 At (w-u)l Fe alta 2 a 2 (yet) ea ( 21 Un-2) | (nary OE) ST] a ge w-ryin-3) Yt sua hrs wR > nee -s)=0 oe BMl Ugg... Gav) ry. Find AT Al i zn! (Man)ong) Oe HBA) Ny tee KI (act) > eae) in 28 9 (1-3-5 ---- (rn) a (a oar gra Azz wt c Fandomerdtot pencito wa bipiiced enn ie < pou thu oma 2 jobs Trond T ny and en wooge mapechely, drum J, get Te Or bs dee UA Koy k Hy Ex + Thre Oe 2 Woy to trowel pom Hyd Banghore: Begs ; Hyd + DAZ: Tht wor A owas to trowel fer Resplere fo Dele Wa ta dancer bowed i‘ cow bt clem2 tw C Scanned with OKEN Scanner m Ro Ny THOSE OMAK 5 Re ee ere b : ? Ns f fore \or par) Cbd ly) Y / tr} RNW = 2x2 -6 / . ] , J Repuired ne: of nos Nott: Sup pou Thur om 3 Jobs Ti Ti Tz er & don ay min, P ous ms petit . Thun Wo. oF wag to da Te TLG4T, ~*~ wen xP mous Q) A reom bos 6 doors in bo mag OTS Coun reun 1K the ron trrorgh au deer gud en Thro wi on difpust door. Th = entering op) room 4 No: wasn to cnrter rcom =< brocgs Te ney worn ts enc The room = $ oougs RNW a ox5 = $0 Wags. * Fundomectal pivupl sf Addiben @ Seppo Thun or 2 jobs To onal Fr while con be dent w malay ond n Wop Heopackitedy « Tet 0, of wow to de So& Iv UU (men) Worn. @ Fra clasnoen Then ow 1B stidunty (10 bow, & givls) the tadur vont t stack @ eprusut ahve from, Sti dis Find te wo ok a a3 T+ WP of woeas tp sulk mprvent abu. from bogs =10 TL = No- 45 Waxy bo caulrct Diforinterhing fren ges = §& RNWN aA T+Hha lotsa cs , = Ret | povediner fo) : . y gold Low “AND UM =) summery gf obovt Dice + f Fon OR UAL iy Fucutactel Pyike a ae leh Noe ; o+ fop-tizr | 4 C Scanned with OKEN Scanner NoWs: Ba nen tn The weg, np SE 4 Ha vy “ | “ (w-v) ol ; “P= ni] : O)mry EO: Spa m 2d (oR) 2p - S 4 . 2 bh (62)1 Ps ee SO TP, =a = 210 (08) 'Py= 2b S * 210 0-3)4 ee “tem mall: Nos of iny echovg (orn ovr fumctions ) fom Ato B by (8) 5 , WB) 2% ROA) “CRI < nlp) i Ta A, Com bA mah pd in wu Tot or con be met with (n>) 1 Cnweuda of zB H é Tr an Ow be mop bad uw oe No-of injections from Ate B (w-ta-1) nog ah — We) Pa Peay, ®Qaxfrriry Be farevi,o, uP No -oy Ty ecbrovy pew Ato 4 No of injection pom At B = “Cp 5 Spo Sue *CAY . a 60 0 ay Neh rycebiony for Ro A UE 4 (A) 4B) bon 4 wi { Me OWA ty powre ble tra it acl by courte i p C Scanned with OKEN Scanner ae Rupe Eubrore cy ettoreet x a Nook pane lecty ony ¢ i as Copper @ Latina, talus ‘oy! gh oo IN , gine BOHN C Whore xbetitiow Ww auovedt ), pel yo The obo gk we mend w eq uiva tut prcleg ep oh blauleg by using nA is we: a worgs a Aa [pournd things —_ — (Ablonks) Tea T* bole com be y-dbaal ub Ww Kn ways Tlot Th Ghat cow fet. ue ow oege ( repetion allaw¢cdl ) 4 ‘ Ta) tat bho cow bidrrel wok mus . Rew DP nen Hee ew we (x imes) pou —— . , nls) {uuwad » Noe of posatbs fun dows pom te By EP CE) \ \ ro \ = pe CACA) =X i n(6)=2h) | naw 3 ' Noo pacing Ons franck omy, je Ate R (A) a aL W a & n(@) - ne ea aon Pa A Jotul roof Fue oo Totnt wos ob ome ome : A= {XB vy Re Lorri crdy Nev of puactions = [per A p,. : wA) 3 i 7 . At & =) we) 2 4 >) Toto peo- + pune Kem , *) 6) wa) = 4 Ale) 2S. Tool morag many one fnctiovds fam A 40K 4 Sp =) bls -120 « SOS > tyr- mp “wy SH u n Pal C Scanned with OKEN Scanner si how mow meas 3 prrra br distri biteal anneng 4 boys whan > yee) we BOY GS mere Thom ne prion () fr bey came GE cu nas ig patie wi) Ne beg gt al KR besa, yew “Py = 24 QW) RNw 4 4-64 Gi) eu 48-4 = 60 R . . No ve chen Allowed Rep ( Ar8, cD gata! priv) . No- ok eee poumutlatons ae n Lf kent Thee gs E ae Sa ok ab Aime whin a porter Ting uw +o be inate cut eke in each omnronserneyk in Ee, | fy: T,= place that pod Urton thing in ony ort bLlark . n lot 1 > blonks) No- ¥ wos - Ti = no - df cur ogngennen ae (aoe) Thevgs We [r-1) blanks Ti and Ty — x > enw=7 ap (vw-) hor a porburlan “ebej ect uw olowgs Mchrdeol in each recomend } “s eG = partrelor obj > "4,8, 0,0, E,F,4& (ut -c= by ) (a uth) + —|<}—- - - =F wey " Ese (E] t > purer as: 6 Py fi * Py, = 19° iG): No- purntehens Ag daft Ahog tahun rn» at a time * wor included UIn-DL f hin a pou ol ow obyect © “aw ‘ ua Gs Pall Pey ' tee I keep orice porta myeck , enw a SP | Remaining Things = 2) Bicwes FF C Scanned with OKEN Scanner (©) How ieee di pd words (our be formed writin Tae Wher, ( Np Mee vwxd * EQUATION”. so tat G) The Wor dy bags with €.- G@) Ware basin with E and ends vib NX. Ui) ards bag in with vowels gud end witr Lomonant bo) og (i) a | en en GL | a hy et ae eee My ; Vowels 25 | Fix. i A RNW = Ip = 3 | BNW 4 bP, a6! | Orponed 27 Remug Uther = 3 | Rew blokes = & I oo --9 Rerroing bless TF - rT a a | Rem Uther = 6 Siam s Ig " (Elov) (aT) iia sh 3/1 foot they Army Oe deny Ory in gle epee cite i phe We ROE Remletasb — SN Wet Tih yy be (aed ton. = 6.3.6 (ten Se Ran blarkes> 6 3 Pe ® Tn bows mon] Boon 5 Bond 3G Cen BA OY Oa col Un om rOD So thet pe ho wh to T= Sho Sy re ate re D car arranged in S| w if conga im S| wong, B_ 8 _R_ BRR — GAP method JrJ th 6 pa Oar oa, Br. = OP, ways, RBNHWA TIL 4 Sloop, 4 14400 x-Alp te seme For “No two” apply |e at wutrod] ~ @ qo rere | wags 5 boys ond S giv OO BS eorrotnteal in = com) R_ BL b, _ Ry Be UTP peace bos ) Tit S| [For 5 Gys) ss) CFov 5 Fv mh © Ranks) Ptpdimpsems Gey = SAS a yy Crete) oe SF Gi 1. y Cem 2(E Pace gir) aaa (sy Woy ¢ RNWo CRG, 4 sifee C Scanned with OKEN Scanner B how many bitprrut sigue ls daw be given wring Ong no, ae flags fem 5 hope + pant Wwlorrs . e JT. 3 ows bg Con be wie {por signet = SP, TL 7 two hss " " w = SPL ’ i Ree” RNW > SPi+ SPL +SP, 4 Spy +S Pp. a S Py “ uy - us (Toho tye) @ Hors meng diffunt mambins oy H digit cow bs horn pom Tu desity 01,0 --. 9 Ay rapety an (iy etlonrd G0 noel allow 7d) — — — Dd AK IOK 10K 10 GQ) ~ oo L L g We TTT =A 4000 Wi 4,7 ®& 2 (wos) io (ceesph 20) 44-84 . BNW RW (vexdudse 0) — ~~ age by 4.4 Py 1 Tu no: utet ous w the teow all ata ee a eke whoa. PREY tie w a = jj) oa things el (€*) ABC Con be oxvanged Us 3) wo oys bon AiR B Com be orronped Un a aR wees (Enz) A*ABRLD & fh CNo + Ay ransemendy ) \ 4 {News?. Tan ne i Len orrntng com ents a ‘Kw hi ppermt prings ou A ot & me of Which “po orc alike Os one kind and’ 4 ant ablile J owrethu kind = ni acy (Ex) AA BBR C ant Cnio-af arreng eno ) C Scanned with OKEN Scanner . o . vost SSUPPA ‘ Niet Orang ements ba thing ethos i am LOMAS ke uct gat no % Lk, ail ; ° t i ' SA 24 Perv | Tess. ' wy gn ® » Drury) aNA NA! — Nevet Arig’ 4 oy (Ape2 a's 23) é VWs i~ “ A . TiC B& No % owrerganenty using Due word “MATHEMA pid~ vowels CLLur tosethr Ww soy Hoy (at) a eax \+ MTUMTCES © & LUKE on =i No: Of Areoungmnrds ia) > 31 = . j a wa Ya nook = ~ rae dons Hos : 6 od ws earch wor “4 a) Trt Ore pee abiichy § subjeds con br orrerged © re tt ~ daosk period ond 0 Crud subjek w cbloted ot ow period nunatna Vvacond ‘ mer eG eS 1 ict (0° 5 / week contd pr mperted TA Gr 6 patets) Herre , ONO eel con be Sc, toy cebsk ome cebj eet whith raperted = ts mol A 1,23 4 Y) How y digit pumbers owe bt fOr" af waked baad om digit “ repeated Sib a id AMR = aaeeia i - (Rp not alle uwred ) as aaa abbot om = Totol — nen C Scanned with OKEN Scanner bow’ os Wwowhith TR arc 4G@ con ba ar rowgach Qroud >No oh pucker Tete SA no des gets ct gogtther ond 2 panole a bys cit to guthu (B&) +R + Bet Be = 4 - juterncl oxy Tay eats Bee arty ed} . up. s - . I,7 Haaps pe givly a Pu 22 4 208. b Tre mrmber os anracuns ements Hy Wr Ana Core de garter t wm nckwu Ww (n=) | ‘ p 2 i i y ACW eet Tithe Cor, we take ~4 one diction, ecthir CW or BD Rad tee wo ] wags iw which (1 ditant diamonds te form o nrckelrer - Ft re Lu ha: No- lg crud or bivwtobens * he AZ pt things tein Fon ok a time ib oP tn ze) oa a Oa Selick nr things prom teeny E Ls Prange Thiat nr Trtngs ground rds 7 CAS RO Berewa “cy Gen! (] host) wl 2 OS! a Pa > n -(ract})licn aq SR Be ‘ Cx Oe (may xi * Xx cau ‘ Can bt ceated Di hos many ng 1% persons out of 2H Pons f fond a Grutor table Pew ner Byte OF “a UL ko. No- 5 ga arlon promctotions K ” a a Stkew : and coor ws MPp Exp zw SP Hy cena we tate only one dir C Scanned with OKEN Scanner ed) How prone necklace Hoth (2 bred cack Con Be meds a ly brads uy vartows wlouns = = wlooae SF Keig N=IL, 2 enw Pry oe PERNT IE KI ZL blx24 BX SKMAVRIRD wy ma ATND bone = Peers) ~ 2 + Rank of Word (Dichovery ovdin) BB -Reek + dre word > Gop! 7 betel ordin J Pe GLO No- ip words bisin, with Dw DL = 2) | NO: Th werds brgin with G9 @RBe=' | No- a wards begin with Gob tt i 4 Rawk of Ths wore GOD 4! Ty wort the Le | move Some | | ry you dot wart te} cS) Rome éf, the Wor “MoTHER’ Lihern twin stop. ! a ~ eticel od 4 E,H,M,0,8,T ho: words agin with BE egy (e=aeane t 7 . = stop “oon “ beer with HOWL os S| eg bigs with MEL = ay (Ma enk ° & gosatk a o eg with MHWL TA (og 5 dort stop “4 & ¢ 4 with MOE-—-_ = 3) wos He words Sigin iH, MOH ~ ~ = 2} uw ” widh MoR — —~ _ = 2) (s+>p) with HOTE —~ _ = 24 witty MOTHER = 4 Rowk + si+ SI tala ap erie By + 3pa di + | % Jaq aes E SS (Ron) | C Scanned with OKEN Scanner xt COUNIN (fade) “7 oy Libel ovelu = ¢,C,H,2,N,9 Wes sk words brgin with e*ct-~—-—-74) no Bf weyds brgin wilh CH - - - = 4} "g Cy ---- = 4! CN - & - - 7 44 C0¢ HI N= 4 Rank 9 4(4[ yi a 99 (© BANDA Cenk) w habeed adit AAA, BY NLN | ner of wordy begin with AGB —— = BS) 2121 | mo ef werds baer uit, BAA 2 EL 2\ G2 BANANA eee it ; in NH BANAAL = 0-2} Prvagenge werds btgin BA 4 @~ uaa | BANANA = 14 ater Rank a FR rotate lel = 2S aK Ex ponunt of pee number Un coal (Epls1)) en) (Edi ay = Ag-d-b-4 Exo) cls Speuegeay | = ahegi she z 2?-ah.g! | | Exponent Br 4 28 ExCal)= 3 + Byiso 2 Elsie | Ei Cat)e | 5 ey ft E,(m) = J n “ ' ix P l . P a + as tote (eX. pie pant CI qQrr ) any. ec= (3)+0h)+CS]+-- > TI +H = 3 a E, el) = ( Ex ponent of Zw 10] =) 7 E,Ue0l) = [f)-[H]- (5]> Atl +s. . 4, C Scanned with OKEN Scanner ol = 2a BFS VP Max tx. pers he L Mox will ba porter Sp 2 s0 tet Eber) Een [ 2] J+ [2])- L?]-[#]}= S+2+ [> & ports DF D will be mort 4 pom cK = 8, Poo Ty BDL. n £,33)) 9 [2\- | =|. [>| atae (2 7 it Bear rari a xy f | a 2 WN = 20n14 XBR KH i . 201 AON = 1 pox la Kx H- KM RHO KBD) to} — (ORM K m= Prd ey aA Exporud a? Zim 20 - Expomnd of 2hR lof 4 E20!) 5 E, (el) 9 (F) | SHS] - [2\+(2] +4] Lv 2 ere ® (Oy € Reqs t Dy, e a by oe. N = 13 749 seg - Ex D Pein poment 4, 16 me D Find the noo} nou UW 601 , : Soo o= 2x5) _———— h No zerwey a No-of tors ic ne =a ie mb Ps \ ~-E,f0o}) )a( so]. [ 2]- (2) {21{] aoa ah 10 75 we atte wot PUrV“r + > ae | ert ——— 74 Bo + OS Bhs _ Es (b0}) “[2\-(] eo oe ieee FM Ss 2S 2 S gol a ag % gee > ~-” ( —t Sat 20 : gs ga 7 10" Aus a] RO’ Of LOY ‘i “@) \ te : k ‘ : A bie 7 Pome oy 5 curectly os 25 will ba over le L, yi, C Scanned with OKEN Scanner | niiple =f Incluken circ Exclusion » 5 ly n(AURBYL) = n(n Fula) Daley — BD eA) d egret > + n(AuBYC) =) Soo + 223+ 20 —~1eb-bb- 109 TFT 83 7 73y the hove problem no: a +e integers Which ou not déinihk ae 21%,5- = | 7 neanw ae) = & (Av eee) | ACA) = wle)~ HCA) | ° uv) _ (Aus vo) | Universal | = 1900 -73Y = 23Gb bac mak ch OE peamongemenks “4 Tn won’ Wittens and Loree ponding envelopes (om Lkben WW tade envelope) go that no Utter wy pland ™ correct envilo “w Sn ve Oe semi ]=r | P aC 3 r Zz) cre ” si Leb w Cetlers br dumoll by i ek Se Let Aj dunctids st of clutibution 4 Litter Te crwelobe so . Thet it Litter w plaud UW Lorvespondang tetey envelope > | t= Uh the placed correct, hlay= tO] | (n-O\ : Rem eining Litter (n-1) MAA AL) = (xix (-dl \ Can be placed Gr Ca-) env. um Utlen peut corre thy - 2) ana-ay Ley in (1-1) env: “(ANAS A AK) = thet (r-2)| | aa n(AnA AAy An) = oY) 7 PCA YALA) 1 L \ er [ Sac) -S aaj nay)t- + hin CA MALO--- A.)| 1 ij [ *C, (n-yl —-"C (w-2)i + + (aye man (w-n)t] \ TOA 4 wt wo. + Egret _. |, xa zy Se wt C Scanned with OKEN Scanner U3 ory os in ; bo ont cach Ww ornib , abi, Tra Batty art OP6% Me ome Ban. Laukd be placenta 4 a boll coe wet 5 do AkY drouth of, iby OVO, Gy Lor. ~ ~ atfie bet | 4 9 Bae LES 3) at ? a Thou ge 4 by oly of cli fpant Us(park Gro 4 boxy “| Sana os Trott sk Th bolle. dnd Tha member oh ts an worshipping Pilea err hag eadth ot pandem +» Tr how werd ney athuork ond atmo thru gt Aue correct, bogs: > C17 one Lorvrect [ovly) ENN TE De AD 2S BITS ZZ Selechow of om beg erred bom 9 bogs cn. 7 peo my correc BNW 4 IC, De A @ pixuy a AY (3-7 ee ee wor recK @N-W 1,7 bu ® Wx A= BT plow, Adel oll > USiMCe we & Cor C3) 7 Tort weg! © 3044 Fyre mart oa 4h q 13 ( — a dearvors abl abot ranged of Son out ; ) Y cea Meine o my al Yams w 47 ale %& Mobi Coad C Scanned with OKEN Scanner