00020002010014Basic Statistics.ACT000802001001 Bar Graph.EAC0100000003bbÉ 01 Bar Graph.EAC†Basic Statistics.ACT†,†/ ˆ<†@Š Ž †P†kE †(Œ' [ˆm ’j†ŠQŽ Ž)!Our team had a sales competition.[ŒH ŒPSˆ(Œ\GregŒ 30ŒqDiane’8ŒDmitri’1’Nch”2Œ´CanyonZ49\ŒÌTableåˆÙ‡!å4N SpreadsheetSІˆÈ©†ä†ˆ @-ˆ"†  ˆ† @ˆ;!GregŽ DianeŽ DmitriŽ'Sach†!CanyonCTotal†T”,les†` †…†ŒMˆs–&¤¤& ¤91ˆLˆ l†ê !ŠÚ%Œ#44 ‡ !†#ˆˆEdˆ‘†ÁŠþÿøŒ€‰’^š;†ð;ÜvŠ2†ß!‹d†ø–7 €ˆ †í†… 4˜;Ð;†&‡9ŽŒR4Œ`PŒgp’$ˆ6ˆ­ Œ†NAI–‡O‡x[†×† @Open the Table, selectŠsales numbers and drawŠBar graph.[†ˆ  Try your own.[Œ# Œ+SˆXŒ7GregŒ 59ŒLDiane63ŒDmitri-45’Nch’2ŽCanyonZ17\Œ§Šæ刴†¸åоLN SpreadsheetSŠŠáˆ2Ȇ †äŠ< ˆ @ˆ †‰ @ŒZeAct02001302 Circle Graph.EAC010000000342É 02 Circle Graph.EAC†Basic Statistics.ACT†/†2 ˆ?†CŠ Ž †S†kE †(Œ'[ˆp ˜m†ŠTŽ Ž'Our team had a sales competion.[ŒF ŒNSˆ&ŒZGregŒ 30ŒoDiane’8ŒDmitri’1’Nch”2Œ²CanyonZ49\Œ. SpreadsheetåˆÝ‡(È䆆ˆ @-ˆ"†  ˆ†@†0GregŽ DianeŽ DmitriŽ'Sach CanyonˆCˆK”#les†  †’ˆ'–&¤¤& ¤91†×Š†×ˆÛˆßŽŒ†ŽŠ5fffff† `Ž g† 0ŠUŠ)™™™™™Š† G ( ‡_[‰COpen the Table, selectŠsales numbers and drawŠ-Circle graph.[ŽITap†. area to fi†:what percent eachš^ is ofЇtotalŒ{˜Yˆb Try your own.[Œ| Œ„Sˆ´ŒGregŒ 25Œ¥Diane43ŒDmitri-38’Nch’5ŽCanyonZ19\Œ. Sp†òdsheet刺†¾È䆆 @ˆ †Šˆ[†#†-eAct02001003 Histogram.EAC010000000874É 03 Histogram.EAC† Basic Stat†ics.ACT†,†/ ˆ<†@Š Ž †P†kE †(Œ' [ˆm ’j†ŠQŽ \Œ Data TableÔˆ+†sÊŒ†ˆN&%FinaFormà$N†Graph2D†% 3Š ˆLISTSYSˆ$†@4ˆ< Modify XˆPˆ<STATCALC |ˆdˆŒ< „\ˆx SequenceˆŒ,ˆxSheetˆO |’ŠŒˆ’ olveEqˆ´†€`wrˆ´(Upˆ’tupFLG1 (Š<†Lis†{HD‰ˆPic†ŒÜViewWind°ˆŒ_osve†v‡5Ìx䉉،ä’ä ä’ð´ä’üÈ䈾‰g ‰ †ä† † ‡<†˜X’ ’’,’’8’’D’’P’’\’’h’’t’’€’’Œ’ˆ¾Šß˜’!’¤†"†°†#†¼†$†Ȇ%†Ô†&†à†'†ì†(†ø†<)‘† !*‘¤¸†ä+††  †,Ž5-†4†.†@†0†L†1†X†2†d†3† p’ˆnŠ£|† 5†ˆ†E†”†F† †H†¬†I†¸†J†ĆK† Ð’ˆæ‹C܆ M†è†N†ô†² O‘|‰…ŒP†Å †Q†Å‡R‹¸†Å$††À†Ô S††ˆ±T†C<†]‡>H†AÔ ˆ^<†ë Š_P ‡]`dˆx†fax‰8bŒ‰d † t†1e´‰Š”È’´•x”ðÍPŠÎðŠЈˆð†¸ב,‰"ŒØ‘@ˆæ† Ù‘Tl’Ú‘hx† )Û‘|„‘ Financiaˆ=Format †† †Œ†ˆ)˜ systemä]list’^]=’_Œ’`Šaˆ #b~Žu/ÂŽŽž¾ þ@þ€þÀýÂ/œ ÿÿ@ÿx‡¸Žž8ŽŠ–V¸¨øˆµ†† a‡ seq_h†¥b† NewFolde‹5ˆ3 ’ šË†0’ŠÊ ” —p†††Mî<‰¼´ö Œ©ŠŒö<ö<þxþðÿ,ÿh§¤‡‘4)‡R]‡j†† †Œ&Œ,’ ’,† †0†!@†@PSheet1ú b^Š2ž3ž 4†5ž ŒH3DÊ|èš|š†††Š˜| “i™” ™‰G‰K† %Š Ž ˆ†kE ‰eŽÀ‰`†$«d«y‰´†`†† † Š” †#’$†(œ†AŠ ˆ'Ž `– PZÆ$´$’¡– ”x ™p”0–„EEEEEE†ñ ˜’0Y™`¬0™ (1…0qy`ˆä#Y‡uYƒŠH–˜œœx®Æ$ÈHˆ’!†’ ’¢´#–HþTú‰ØÆ Œ¸†¼†«†Ç$K<†H†T†`†l†x†„‡o윆à@<ñ–– ˆš‘4– š`˜lˆ ‘¸ œ†Ýކ+Ž ŽŽ†† ††$†0†<† Hˆˆ'–L† † –†F–†g’<Ðtˆ8– ²€°˜¨HˆÈ˜Ô™ ”0 `Rcx”t‡> ˜’e5‰yˆ” – œ˜ÀX†[ˆ JOpen the Data Table and tapŠGraph button. SetŠ-interval’+OK.ŽR 4You will fiˆH†D frequency†thŠ Trace functi†YŽŽˆ–ˆ— Try your ow’ 3Experiment”HHistogram by changingŠÐd†Ð.eAct02000f04 Boxplots.EAC0100000010acÉ 04 Boxplots.EAC†Basic Statistics.ACT†+†. ˆ;†?Š Ž †O†kE †(Œ' [ˆli†ŠPŽ Ž-Open the Data Table and tapŠGraph button.\ŒN ”,Ôˆ`†§ÊŒºhS Graph2D@† †Š3ŠT† ˆLISTSYSˆ`4N†Modify†; ”†($ˆ< STATCALC ¸†Uˆ(ˆŒ< À\ˆ< Sequence†<,ˆxSheet†ŠH†|’ŠŒÄ’olveEq†´ˆ´LwrˆÍ (UpˆP’ tupFLG1\†<(Š<†Lis†{„†dD‰ˆPic†ÈÜ ViewWind솉,äб‡@xä’Œä’  ä’,´äˆ2‹8Èä’’ÜäŽx P †ä† † \’’h’’t’’€’’Œ’’˜’’¤’’°’’¼’ ’È’!’Ô’"’à’#’ì’$’ø’%‘’&‘,’'‘@ˆæŒ(‘Tˆ Œ)‘h4’*‘|@’+‘L’,‘¤X¸†ä-†d†  †.’p’0’|’1’ˆ’2’”’3’ ’4’¬’5’¸’E’Ä’F’Ð’H’Ü’I’è’J’ô’K‘‰ ŒL‘ ’M‘,’N‘@$’O‘T‰6ŒP‘h<’Q‘|ˆ¾ŒR‘T’S‘¤`’ˆl† †ä]†† xD ˆ^¼†-Š_(À’`<Ä’aPÈ’bdÌ’dxІTŠ”Œ$’ • 0’Í´<’ÎÈH’ˆZŠßTð††ˆŒ!†” system‰list’‡]=’‡‰,’‡‰(’‡ ‰$’‡~o/ÂŽŽžº /ˆŽž¾ î8þpþ°þðÿ0ÿp¡°/†ŽŽž¾ þ@þ€þÀÿÿ@ÿx‡¾/ÂŽŽž¾ þ@þ€þÀÿÿ@ÿx/ÂŽŽž¾ ”†† a†W seq_histb† NewFoldeŒn† †xúŠ} systemä]l†0’^]=” –¨††î<ˆxîxö<þx¦´systemä^]=/ŠŒ’,]listö<ö<þxÈð††† †’ ’,† †0†@†@PSheet1ú b^Š2ž3ž 4ž 5ž ŒH3DŒ|† †0†@†PSheet1è b^Š2ž3ž 4ž 5ž †lŠX3D†v Іi™” ™††Š Ž †® ¸Dkäûxˆ¹†°ˆÀ ††$’S’\¢œ†jD²<‡Žh†(žŽ `– PÝÆ$´$“$–  ‘=`†Ž ˜ HH† ™€`” –0F ˜ (1…0qy`ˆH#Y‡uYƒ†T ˜’k– ’Hˆ „ Æ$ÊH  À! °´þaà †Œ˜ ª†† ††$†0†<†H†T†`†l†x†„††œ†¨†´†À†̆؆LäŽ[PŒ œ`– ””$–0–0p– – lˆH–H – – @”l–œ– €”T–œ0”0–Ø«q­X™ŽPˆt†0 P†Ž œ† ˆ” ˜–`–$ ™†ŒV[ŠICXIn the Analysis menu, tap Trace. You will find Min, Qìñ, Med,Qìó aˆax byˆ6pingŠQŒ_cursor button.[ŒuŽCompareŠ‚graphs.\Œ˜Two Lists of DataÔˆ<†@ÊðS Graph2DT† †Š3Šh† ˆLISTSYSˆt4N†Modify†; ¨†($ˆ< STATCALC ̆Uˆ(ˆŒ< Ô\ˆ< Sequence0†<,ˆxShee†]†Œ\†|’ŠŒØ’olveEq†´ˆ´LwrX†Í (Upˆd’ tupFLG1p†<(Š<†Lis†Ø˜†dD‰ˆPic†ìÜÜViewWin†L‡0‰,äб†x䊊(Œä’4 ä’@´ä’LÈä’’ÜäŽx d †ä† † p’’|’’ˆ’’”’’ ’’¬’’¸’’Ä’’Ð’ ’Ü’!’è’"’ô’#ð‡Ž$‘ ’%‘‰Œ&‘,ˆ2Œ'‘@0’(‘T<’)‘hH’*‘|T’+‘`’,‘¤l¸†ä-†x†  †.’„’0’’1’œ’2’¨’3’´’4’À’5’Ì’E’Ø’F’ä’H’ð’I’ü’Jð’K‘’L‘ ’M‘,,’N‘@8’O‘TD’P‘hˆ ŒQ‘|\’R‘h’S‘¤t’T‹¸€† †ä]††Œ†´ ˆ^@’_(ô†Š`<ø’aPü’bd†|Ždx†TŠfŒX’” ¬’´•´¸’ÍÈÄ’ÎÜÐ’ˆ ŠóÜ‘ˆ…†‰ˆŒ!†” system‰0list’‡,]=’‡(‰@’‡$‰<’‡ ‰8’‡~ƒ/ÂŽŽž’ /ÂŽŽž¾ þ@þ€þÀÿÿ@ÿx/Â/ŽŽž¾ þ@þ€þÀÿÿ@ÿx‡¸/ÂŽŽž¾ þ@þ€þÀÿÿ@ÿx‡¸/ŠŽž¾ Â@†† a†n seq_histb† NewFoldeŠ…ˆ3 †úŠ” systemä]l†0’^]=” –À††ö<”<†hÖxˆ´î´ö<systemä]list’^]= †,/ŠŒö<þxþ´äð† ††† †’ ’,† †0†@†@PSheet1ú b^Š2ž3ž 4ž 5–@heetSˆ3D††† †0†@†PŠ$ 1è b^Œ42ž3ž 4ž 5ž ˜|†x І‘i™” ™††Š Ž †¾ ¸Dkäûxˆ½ŽÀ ††$’S’\¢œ†j ²<‡Žh†(žŽ `– PÝÆ$´$“$†€’ B”Ž# ˜ qB…qB††5 ™d”<F¬0^ ˜ (1…0qy`ˆH#Y‡uYƒ†T ˜ƒ– xˆ ®Æ$ÚHœ‡0” "*ž¢°´àHÖx†Œ˜ °¢1 †† ††$†0†<†H†T†`†l†x Œ7Ž œˆ ” `–0”$€®$p¬$šTޝˆlà´–x˜´@”À”x–̘œ˜$˜H–›–ü£©x ††$†0† œ`– €” ”$p”0†D†žT”T0”T–T”`–`ŽŠ” Ž-¢`9G6„!†‰ ™QŠÏ[Š×-Open the Data Table and tapŠ Graph button.Ž5ˆ=‡% Try your ow’*ChangeŠTnumbersŠQfi†V Qìñ, Med,† ó.eAct02001705 Mean/Median/Mode.EAC010000001c3aÉ 05 Mean/Mediˆode.EAC†Basic Statistics.ACT†3†6†@ˆC†GŠ Ž Ž$ ]E Ž'[ˆ4 q†ŠXŽ Ž" When the data is {1,2,3,4,5,5,6}\ŒA Box PlotÔˆQ†UÊŒ³`S Graph2DX† †Š3Šl† ˆLISTSYSˆx4N†Modify†; ¬†($ˆ< STATCALC ІUˆ(ˆŒ< Ø\ˆ< Sequence4†<,ˆxSheet†Š`†|’ŠŒÜ’olveEq†´ˆ´Lwr\†Í (Upˆh’ tupFLG1ˆk(Š<†Lis†{œ†dD‰ˆPic†àÜ ViewWind†‰,äб‡@ xä’,Œä’8 ä’‰Š´ä’PÈä’’ÜäŽx h †ä† † t’’€’’Œ’’˜’’¤’’°’’¼’’È’’Ô’ ’à’!’ì’"’ø’#ð’$‘’%‘ˆ¾Œ&‘,(’'‘@4’ˆ‹W@’)‘hL’*‘|X’+‘d’,‘¤p¸†ä-†|†  †.’ˆ’0’”’1’ ’2’¬’3’¸’4’Ä’5’Ð’E’Ü’F’è’H’ô’I܈åŒJð ’K‘’L‘$’M‘,‰ŒN‘@<’O‘Tˆ–ŒP‘hT’Q‘|`’R‘l’S‘¤x’ˆF„† †ä]†††t ˆ^†Š_(’`< ’aP’bd’dx†TŠvŒl’ w x’ˆ Š·”ÈyȈȌzÜœ’{ð¨’|‘´’}‘À’Ž‘,Ì’‘@Ø’‰J‹Wä’‘‘hð‰mŠð’‘h‰hŒ(“‘@‰@Œ”‘¤† †ä•†( ŠÍ’4’Î’@’Ð’L<†ŒŒ!†” systemä]list’^]=’_Œ’`Œ’aŒ’b~ŽÏ®ÁŽŽž¾ þ@þ€ÒÀ®Á†ŽŽž¾ þ@þ€þÀÿÿ@ÿx‡¾®ÁŽŽž¾ þ@þ€þÀÿÿ@ÿx®ÁŽŽž¾ þ@þ€þÀÿÍ@†† a‡o seq_histb† NewFolde†‹Š ‰– systemä]l†0’^]=Œ em®ÁІ†systˆä]list’^]= ž<ˆMö<ö<þxþðÿ,õhmä]listsysteˆ^]=®ÁŠŒ’,Ø<††† †ŒbŒh’ ’,† †0†@†@PSheet1új‹^Š2ž3ž 4ž 5ž ŒH3DÊ|èš|š†|š†|š†|š˜| “i™” ™‡€‰ƒ‡‡Ö]¼ÿ„† ††$Š!Š&’ ¤˜”D²<’h†(žŽ `– PŠÆ$´$’Ñ– ’é ™”l"Œ„‰a‰a‡% ˜€–`’ œ0™<(1…0qy`ˆÌ#Y‡uYƒˆl˜–˜œšH”œš†– ˜Æ$’’¢Ä#ˆ°þaþ ¾ßŒ¸‡L ††$†0†<†HÔœ†È– ––ø– Š –‘·†Œ†† ††$†0ˆˆœ– –†;’ –’] qB…qB†Š `z† fY†%VpŠ0y”p‚…Š<˜„˜`Ȉ=ˆ@˜¤Pˆ\Dˆ ™˜$¬`–H ™†^ŠÇ[‰G-Tap the Graph button andˆn TraceŠ data.Ž5\Œ= Calculatorˈ†ß“tÔRˆsum({1,2,3,4,5,5,6})RŽ 26–.mean¬/’0ŒY7š8ode¸g5–.medi°hŒ·4–ĈÎÀS Graph2D,† †Š3Š@† ˆLISTSYSˆL4N†Modify†; €†($ˆ< STATCALC ¤†Uˆ(ˆŒ< ¬\ˆ< Sequence†<,ˆxSheet†Š4†|’ŠŒ°’olveEq†´ˆ´Lwr0†Í (Upˆ<’ tupFLG1H†<(Š<†Lis†{p†dD‰ˆPic†´Ü ViewWind؆‰,äб‡@ôxäŠ ŠŒä(  ä<´äP$Èäd’ÜäŽx < †ä† † H’’T’’`’’l’’x’’„’’’’œ’’¨’ ’´’!’À’"’Ì’#’Ø’$’ä’%’ð’&’ü’'‘@’(‘T’)‘hˆ¾Œ*‘|,’+‘8’ˆ‹§D¸†ä-†P†  †.’\’0’h’1’t’2’€’3’Œ’4’˜’5’¤’E’°’F’¼’H’È’I’Ô’J’à’K’ì’L’ø’M‘,’N‘@’O‘T’‰^‹k(’Q‘|‰ŒR‘@’S‘¤ˆ–ŒT‹¸X† †ä]††d† ˆ^’h’_’l’`’p’a’t’b’x’”’|’Œ•’ˆ’Í’ˆ2ŒÎ’ ’Ð’¬Ü††ˆŒ!†” system‰list’‡]=’‡‰’†ü‰’†ø‰’†ô~[)ÂŽŽž¾ ¤@)ÂŽŽž¾ þ@þ€þÀÿÿ@ÿx)Â)ŽŽž¾ þ@þ€þÀÿÿ@ÿx‡¸)ÂŽŽž¾ þ@þ€þÀÿÿ@ÿx‡¸)ŠŽž° †† a†F seq_histb† NewFoldeŠ]ˆ3 ’ systemä]l†0’^]=” –˜††î<ˆxö<þxìðÒ´ em)ŠŒsystˆä]list’^]= ö<þxþ´<† ††† †’ ’,† †0†@†@PSheet1ú…^Š2ž3ž 4ž 5ž ‡›ŠX3D´|PSheet1è…^Š2ž3ž 4ž 5ž ŒH3D Šˆ i™” ™†† Š Ž Š8Ö]¼ÿ„† ††$’S’\¢œ”D²<‡Žh†(žŽ `– PÝÆ$´$“$– p”x” ,ˆˆ  ™€ `” ˜$’.ˆ>(1…0qy`ˆH#Y‡uYƒ†U ˜–0– šH®Æ$ÊHš©š¶´¨5°´þaþ ‰¼†Œ˜ °˜’ ®`–$ ™†OŠq[Œ;†ˆD Try your own.Ž" The data is {2,1,3,4,2,5,6,7,3}.\ŒE Box PlotÔˆU†YÊŠ†ÛÀS Graph2D,† †Š3Š@† ˆLISTSYSˆL4N†Modify†; €†($ˆ< STATCALC ¤†Uˆ(ˆŒ< ¬\ˆ< Sequence†<,ˆxSheet†Š4†|’ŠŒ°’olveEq†´ˆ´Lwr0†Í (Upˆ<’ tupFLG1H†<(Š<†Lis†{p†dD‰ˆPic†´Ü ViewWind؆‰,äб‡@ôxäŠ ŠŒä(  ä<´äP$Èäd’ÜäŽx < †ä† † H’’T’’`’’l’’x’’„’’’’œ’’¨’ ’´’!’À’"’Ì’#’Ø’$’ä’%’ð’&’ü’'‘@’(‘T’)‘hˆ¾Œ*‘|,’+‘8’ˆ‹§D¸†ä-†P†  †.’\’0’h’1’t’2’€’3’Œ’4’˜’5’¤’E’°’F’¼’H’È’I’Ô’J’à’K’ì’L’ø’M‘,’N‘@’O‘T’‰^‹k(’Q‘|‰ŒR‘@’S‘¤ˆ–ŒT‹¸X† †ä]††d† ˆ^’h’_’l’`’p’a’t’b’x’”’|’Œ•’ˆ’Í’ˆ2ŒÎ’ ’Ð’¬Ü††ˆŒ!†” system‰list’‡]=’‡‰’†ü‰’†ø‰’†ô~[®ÁŽŽž¾ ¤@®ÁŽŽž¾ þ@þ€þÀÿÿ@ÿx®Á®ŽŽž¾ þ@þ€þÀÿÿ@ÿx‡¸®ÁŽŽž¾ þ@þ€þÀÿÿ@ÿx‡¸®ÁŠŽž° †† a†F seq_histb† NewFoldeŠ]ˆ3 ’ systemä]l†0’^]=” –˜††î<ˆxîxö<þxδ em®ÁŠŒsystˆä]list’^]= ö<þxþ´<† ††† †’ ’,† †0†@†@PSheet1új‹^Š2ž3ž 4ž 5ž ‡›ŠX3D´|PSheet1èj‹^Š2ž3ž 4ž 5ž ŒH3D Šˆ i™” ™†† Š Ž Š8Ö]¼ÿ„† ††$’S’\¢œ”D²<‡Žh†(žŽ `– PÝÆ$´$“$– p”x” ,ˆˆ  ™€ `” ˜$’.ˆ>(1…0qy`ˆH#Y‡uYƒ†U ˜–0– šH®Æ$ÊHš©š¶´¨5°´þaþ ‰¼†Œ˜ °˜’ ®`–$ ™†OŠq\Š; Calculatorˈ)†ßŽ•RˆQŒ.Œ«ÀS Graph2D,† †Š3Š@† ˆLISTSYSˆL4N†Modify†; €†($ˆ< STATCALC ¤†Uˆ(ˆŒ< ¬\ˆ< Sequence†<,ˆxSheet†Š4†|’ŠŒ°’olveEq†´ˆ´Lwr0†Í (Upˆ<’ tupFLG1H†<(Š<†Lis†{p†dD‰ˆPic†´Ü ViewWind؆‰,äб‡@ôxäŠ ŠŒä(  ä<´äP$Èäd’ÜäŽx < †ä† † H’’T’’`’’l’’x’’„’’’’œ’’¨’ ’´’!’À’"’Ì’#’Ø’$’ä’%’ð’&’ü’'‘@’(‘T’)‘hˆ¾Œ*‘|,’+‘8’ˆ‹§D¸†ä-†P†  †.’\’0’h’1’t’2’€’3’Œ’4’˜’5’¤’E’°’F’¼’H’È’I’Ô’J’à’K’ì’L’ø’M‘,’N‘@’O‘T’‰^‹k(’Q‘|‰ŒR‘@’S‘¤ˆ–ŒT‹¸X† †ä]††d† ˆ^’h’_’l’`’p’a’t’b’x’”’|’Œ•’ˆ’Í’ˆ2ŒÎ’ ’Ð’¬Ü††ˆŒ!†” system‰list’‡]=’‡‰’†ü‰’†ø‰’†ô~[ ÂŽŽž¾ ¤@ ÂŽŽž¾ þ@þ€þÀÿÿ@ÿx  ŽŽž¾ þ@þ€þÀÿÿ@ÿx‡¸ ÂŽŽž¾ þ@þ€þÀÿÿ@ÿx‡¸ ŠŽž° †† a†F seq_histb† NewFoldeŠ]ˆ3 ’ systemä]l†0’^]=” –˜††î<ˆxö<þxìðÒ´ em ŠŒsystˆä]list’^]= ö<þxþ´<† ††† †’ ’,† †0†@†@PSheet1új‹^Š2ž3ž 4ž 5ž ‡›ŠX3D´|PSheet1èj‹^Š2ž3ž 4ž 5ž ŒH3D Šˆ i™” ™†† Š Ž Š8Ö]¼ÿ„† ††$’S’\¢œ”D²<‡Žh†(žŽ `– PÝÆ$´$“$– p”x” ,ˆˆ  ™€ `” ˜$’.ˆ>(1…0qy`ˆH#Y‡uYƒ†U ˜–0– šH®Æ$ÊHš©š¶´¨5°´þaþ ‰¼†Œ˜ °˜’ ®`–$ ™†OŠq[Ž;eAct02001806 Probability(Coin).EAC010000001dbeÉ 06 Probability(Coin).EAC†Basic Statistics.ACT†4†7 ˆD†HŠ Ž †X†kE †(Œ'[ˆu–r Œs†Š@[Œ ,4Change the number of times you toss and tapŠ%EXE ŒDkey.PRŠŒˆê50îˆ8R†»Ž50–" seq(x,x,1,ˆ`)îaNŠ|Š2Œ£Œ41,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,2†42,23,24,25,26,27,28,29,30,31,3†S3,34,35,36,37,38,39,40,41,42,4†r4,45,46,47,48,49,50RˆrandList(toss,†¦ )îCoinRŒ%c2†½ˆÁˆÅ ˆ$’ š&˜ 1\Œ Plot the Data݈¥†¯Êˆµ èNH%FinaFormô$N†Graph2D 3Š, ˆLISTCALˆ8(ˆSYSˆ†4ˆP Modify €ˆdˆPSTAˆ< C ¤ˆxˆŒ<E ¬\ˆŒSequence,ˆŒSheetˆO4|’Š °’ olveEqˆ´†‹wr0ˆÈ(Upˆ<’tupFLG1H(Š<†Lis†{pD‰ˆPic†´ÜViewWind؈Œ_osve†v‰hŠx䉉‰ŠŒä’  äЉ@† Š´äŽ< $‰& †ä† † ‡g0’’Š›J’H’’T’’`’’l’’x’’„’’’’œ’’¨’’´† †À†!†̆"†؆#† ä’‰J‹Cð† %†ü†5&‘h† '‘|‰†Œ(‘ˆª† !)‘¤,¸†ä*†8†  †+†ED†I,†P†-†\†.†h†0†t†1†€†2†Œ†3†˜†4†¤†5†°†E†¼†F†ȆH†Ô†I†à†J†ì†K†ø†´L‘T† M†Æ† N‘|† O‘(’‰r‹§ˆú†ØQ‹¸†Å@††À†Ô R††L†QS†UX†T†d†]‡S p†U ˆ^ŽÊ_†x†`†|†aŽÚb†„’ˆ‚Š·ˆ$ŠeȬ‡š”ÜÐ’´•ð܆ŸÍ‘è† Î‘ô’ˆFЇDŽב@ ’Ø‘T† Ù‘h$† Ú‘|0† 6Û‘<‘¤ Financial‡¾Format †ˆ †Œ†Bˆ!” ˜ ­ë•`ˆ8eActnaNumberCoinësystemä_ä^’`Œ†aˆ#b~މiÂŽŽž¾ þ@þ€þÀ­Âiœ ÿÿ@ÿx‡¸Žž8ŽŠ–V¸øøˆÈ(†† a‡F seq_histb† NewFolde‹]ˆ3 ’ ’» ]l†0’†À]=” —˜††Šú†<úˆ†îŠþ=ŒC†Œ¬ ŠŒŠU†{,‰]¬<ö<ö<þxþðÿ,åh†systemä]list’^]= ˆ0iŠ6††† †ŽTŽ[Ž ’,† †0†@†@PSheet1úªÚ^ Š2ž3ž 4†5ž ŒH3DÊ|èš|š†††Š9˜| “i™” ™ƒ‡‡‘†Š †kE ‰eŽÀ‰`†$¸ˆ7 †Œ˜ ¤†e†† ²6’$†(œ†AŠ ˆ'Ž `– PÆ$´$’×– ”xI”$–„‘‡ ™”Á ™ ”`˜0™B(1…0qy`ˆä#Y‡uYƒ‡a ˜–˜œšH5®¾$†† Š – ®˜’ ’¤˜°lâIâzâ«ÄÜ2ŒÐ‡@‡`†Ñ$T<†H†T†`†l†x†„††œ†¨†´†À†̆؆ä† ð†)ü†† †,†8†D†P†\†h†$t†)€†Œ†9˜†=¤†°†¼†ȆÔ†à†ì†"ø†0+(4@L†– –††††† ––l†$ †0†@†P†`†p†€†< ”l–Ø–x††Žžˆ —D†nxˆð ˆ… 0Š Œ †X ¦X HS†`”† ”l†¨x†¬†Ž˜:–x2†  $0<HT`lx„œ†¨†´†À†̆؆ä†ð†tü ,8DP\htF€Œ˜¤°¼ÈÔàìø(4@L•†X” †Ÿ%†– ®š$Þ0š$°xølÈ`ÈðùøäÉ Ÿ°Œ'AŽ – Š –– ²0È<˜’ †®)rqB†¬ ™‚)y†¸ —’e5‰† `†u – œ˜ÌYˆ}[Š…Ž.+Open Histogram window and input 1 as HStep.\Œ;’.(Š=1)݇yÊŠ½$N@%FinaFormô$N†Graph2D 3Š, ˆLISTCALˆ8˜SYSˆ†A4ˆP Modify xˆdˆPSTAˆ< C œˆxˆŒ< ¤!\ˆŒ SequenceˆA,ˆŒSheetˆO†Œ|’Š ¨’olveEq$†ˆ`wr(ˆ´(Upˆ4’tupFLG1@(Š<†Lis†{hD‰ˆPic†¬ÜViewWindЈŒ_osve†v‡#-ìxäŠÓ‰øŒä ä(‰Š´äŽ< ‰ †ä† † ‡a(’’Š˜,’@’’L’’X’’d’’p’’ˆù ˆªŠ£ˆ’’”’’ ’’¬’ ’¸†!†Ć"†І#†܆$†è†%†ô†,?&‘h‡{Ž'‘| ’‰†‹“‰JŒ)‘¤ˆn‡¸†ä*†0†  †+†F<†J,†H†-†T†.† `’ˆZŠgl† 1†x†2†„†3††4†œ†5†¨†E†´†F† À’ˆÒ‹̆ I†؆J†ä†K†ð†L†ü†ÈM‘h† N†Ç† O‘‰P†Æ†Ö†ÐQ‹¸†Æ8††Á†Õ R††D†HS†LPŽÂ\†]‡L h†U ˆ^†ˆÊ_†pŒßt†aŽÚb†|†d†5€‡$Še†¤†”†È’´•†Ô† ͆à†Άì¡ø†ªב @’Ø‘T† Ù‘h† Ú‘|(† 5Û‘4‘¤ Financia‰UFormat †ˆ †Œ†4ˆ!” $4ˆ0 eAct/eCoinˆ0systemä^]=–_Œ’`Šaˆ #b~ŽiÂŽŽž¾ þ@þ€þÀ½Âiœ ÿÿ@ÿx‡¸Žž8ŽŠ–V¸èøˆ¼(†† a‡> seq_histb† NewFolde‹Uˆ3 ’ ’¿ ]l†0’ŠÈ ” —††Šò†<ˆòž<]=’8Œ¡ ŠŒŠJ†p,‰ö<ö<þxþðÿ,ÿh§¤‡ešs†™’‹< iІ†† †Œ&Œ,’ ’,† †0†!@†@PSheet1úªÚ^Š2ž3ž 4†5ž ŒH3DÊ|èš|š†††Š˜|† “i™” ™‡{‹K† Š Ž ˆ†kE ‰eŽÀ‰`†$dˆ8†­Œ˜ ” †f†† ².’$†(œ†AŠ ˆ'Ž `– PˆÆ$´$’Ï– ”‘ ™ ”0–„x”shB‡ —`–`6”H˜0™:(1…0qy`ˆä#Y‡uYƒ‡Y ˜–˜œšx®Æ$ˆÀŽ–eŽ ˆ – –’ ’¤°%˜T˜lúUú’öχˆÐ‡( ³,–$ ’$€“h˜<˜H™iTBx9V’‡¨ ™™D@xŠ ’e5‰y`† ’e5‰y– œ†ˆ$Yˆ [Š76Tap Analysis/Trace, finding the frequency of heads or Œ=#tails to calculateŠ4 probability.[ŒhŽIn†W is example,RˆŒŽH†aŒ\tossŽ¥=Ž 21–R¨;50²9†ŠrŒþ Decimal=ap†´x(getright(ans))Œ`Œ**"‹N0.42 M ™–UëeActCoin $2 $0<HT`lx„œ¨´ÀÌØäðü ,8DP\ht€Œ˜¤°¼ÈÔàìø(4@L                                                  Dice Ä< $0<HT`lx„œ¨´ÀÌØäðü ,8DP\ht€Œ˜¤°¼ÈÔàìø(4@LXdp|ˆ” ¬¸Ä                                                            aNumber $2 $0<HT`lx„œ¨´ÀÌØäðü ,8DP\ht€Œ˜¤°¼ÈÔàìø(4@L                                 ! " # $ % & ' ( ) * + , - . / 0 1 2n 2toss 202001807 Probability(Dice).EAC010000001b21É 07 Probability(Dice).EAC†Basic Statistics.ACT†4†7 ˆD†HŠ Ž †X†kE †(Œ'[ˆu–r Œs†Š@[†Vˆ˜Change the number of Œ& times you†rowŠ%d†º =andˆ:n tapŠCEXEŽ=key.oRŠ«‰ 50înR†×Ž50–seq(x,x,1,n)îaNŠ”Š/Œ¼Œ41,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,2†42,23,24,25,26,27,28,29,30,31,3†S3,34,35,36,37,38,39,40,41,42,4†r4,45,46,47,48,49,50RˆrandList(n,1,6)îDiceRŒ"c4,Œ¼2†º6ˆ%ŠÆˆ2ŽÔˆˆ5Š1†5†ˆ*ˆ,2† 6ŽBˆˆ5’8ˆ01\Œ Plot the Data݈¢†¬Êˆ² NH%FinaFormô$N†Graph2D 3Š, ˆLISTCALˆ8(ˆSYSˆ†4ˆP Modify €ˆdˆPSTAˆ< C ¤ˆxˆŒ<E ¬\ˆŒSequence,ˆŒSheetˆO4|’Š °’ olveEqˆ´†‹wr0ˆÈ(Upˆ<’tupFLG1H(Š<†Lis†{pD‰ˆPic†´ÜViewWind؈Œ_osve†v‰hŠx䉉‰ŠŒä’  äЉ@† Š´äŽ< $‰& †ä† † ‡g0’’Š›J’H’’T’’`’’l’’x’’„’’’’œ’’¨’’´† †À†!†̆"†؆#† ä’‰J‹Cð† %†ü†5&‘h† '‘|‰†Œ(‘ˆª† !)‘¤,¸†ä*†8†  †+†ED†I,†P†-†\†.†h†0†t†1†€†2†Œ†3†˜†4†¤†5†°†E†¼†F†ȆH†Ô†I†à†J†ì†K†ø†´L‘T† M†Æ† N‘|† O‘(’‰r‹§ˆú†ØQ‹¸†Å@††À†Ô R††L†QS†UX†T†d†]‡S p†U ˆ^ŽÊ_†x†`†|†aŽÚb†„’ˆ‚Š·ˆ$ŠeȬ‡š”ÜÐ’´•ð܆ŸÍ‘è† Î‘ô’ˆFЇDŽב@ ’Ø‘T† Ù‘h$† Ú‘|0† 6Û‘<‘¤ Financial‡¾Format †ˆ †Œ†Hˆ!” ˜ ü`3ˆ8eAc†J aNumberŠ/eDicegsystemä_ä^”`Œ’aˆ#b~މiÂŽŽž¾ þ@þ€þÀ­Âiœ ÿÿ@ÿx‡¸Žž8ŽŠ–V¸øøˆÊ'†† a‡F seq_histb† NewFolde‹]ˆ3 ’ ”º]l†0’^]=” —˜†††üt†<üˆ†íŠý=Œý†Œ¬ ŠŒŠU†{,‡]¬<ö<ö<þxþðÿ,åh†systemä]list’^]= ˆ0iŠ6††† †ŽTŽ[Ž ’,† †0†@†@PSheet1úªÚ^Š2ž3ž 4†5ž ŒH3DÊ|èš|š†††Š9˜| “i™” ™ƒ‡‡‘†Š †kE ‰eŽÀ‰`†$¸ˆ7 †Œ˜ ¤†e†† ²6’$†(œ†AŠ ˆ'Ž `– PÆ$´$’×– ”xI”$–„‚‡ ™˜À–H˜0™B(1…0qy`ˆä#Y‡uYƒ‡a ˜–˜œšH®2`¾$†† Š – ®˜’ ’¤˜°lâIâzâ«ÄÜ2ŒÐ‡@‡]†Î$Q<†H†T†`†l†x†„††œ†¨†´†À†̆؆ä† ð†)ü†† †,†8†D†P†\†h†$t†)€†Œ†9˜†=¤†°†¼†ȆÔ†à†ì†"ø†0+(4@L†– –††††† ––l†$ †0†@†P†`†p†€†< ”l–Ø–x††Žžˆ —D†nxˆð ˆ… 0Š Œ †X ¦X HS†`”† ”l†¨x†¬†Ž˜8–x2†  $0<HT`lx„‡œ†¨†´†À†̆؆ä†ð†ü ,8DP\htE€Œ˜¤°¼ÈÔàìø(4@L—PŠÔ².†– ˜–– ®$–®0˜`˜l°˜T°¨°´˜„† œ†0† ü±† ˜0ÉŒž¨ŒJ†TIŽ ˆ – ––®°H˜T˜’ †®– ` !&1W‰†¸ ˜’e5‰yˆ” – œ˜ØYˆ[‡EˆŒ Open the Histogram Žwindow and input 1 as ŒAHStep.\Œ’=(Š=1)݇®ÊŠÐÀN@%FinaFormô$N†Graph2D 3Š, ˆLISTCALˆ8˜SYSˆ†A4ˆP Modify xˆdˆPSTAˆ< C œˆxˆŒ< ¤!\ˆŒ SequenceˆA,ˆŒSheetˆO†Œ|’Š ¨’olveEq$†ˆ`wr(ˆ´(Upˆ4’tupFLG1@(Š<†Lis†{hD‰ˆPic†¬ÜViewWindЈŒ_osve†v‡#-ìxäŠÓ‰øŒä ä(‰Š´äŽ< ‰ †ä† † ‡a(’’Š˜,’@’’L’’X’’d’’p’’ˆù ˆªŠ£ˆ’’”’’ ’’¬’ ’¸†!†Ć"†І#†܆$†è†%†ô†,?&‘h‡{Ž'‘| ’‰†‹“‰JŒ)‘¤ˆn‡¸†ä*†0†  †+†F<†J,†H†-†T†.† `’ˆZŠgl† 1†x†2†„†3††4†œ†5†¨†E†´†F† À’ˆÒ‹̆ I†؆J†ä†K†ð†L†ü†ÈM‘h† N†Ç† O‘‰P†Æ†Ö†ÐQ‹¸†Æ8††Á†Õ R††D†HS†LPŽÂ\†]‡L h†U ˆ^†ˆÊ_†pŒßt†aŽÚb†|†d†5€‡ ¤Šeȉr”ÜÈ’´•ðÔ†•Í‘à† Αì† Б, ø’ב@† Ø‘T† Ù‘h† Ú‘|(† 5Û‘4‘¤ Financia‰UFormat †ˆ †Œ†4ˆ!” ‡3ˆ0 eAct/eDiceˆ0systemä^]=–_Œ’`Šaˆ #b~ŽiÂŽŽž¾ þ@þ€þÀ½Âiœ ÿÿ@ÿx‡¸Žž8ŽŠ–V¸èøˆ¼(†† a‡> seq_histb† NewFolde‹Uˆ3 ’ ’¿ ]l†0’ŠÈ ” —††Šò†<ˆòž<]=’8Œ¡ ŠŒŠJ†p,‰ö<ö<þxþðÿ,ÿh§¤‡ešs†™’$^]= iІ†† †Œ&Œ,’ ’,† †0†!@†@PSheet1úªÚ^Š2ž3ž 4†5ž ŒH3DÊ|èš|š†††Š˜| “i™” ™‡{‹K† Š Ž ˆ†kE ‰eŽÀ‰`†$dˆ8†­Œ˜ ” †f†† ².’$†(œ†AŠ ˆ'Ž `– PˆÆ$´$’Ï– D@Žé ™’0–„w&1W‰G‡ —`”¨V”T˜0™:(1…0qy`ˆä#Y‡uYƒ‡Y ˜– ˜œšx®Æ$ˆÀŽœ*Ž ˆ – ’ ’’ ¤°%˜T˜lúUú’öÏ ŒÐ‡(‡i†Ù$]<†H†T†`‡l™LUV“p“|>fh“ˆ"$“”w€“ 36“¬ˆ’“¸DH†’  † † ††$†0†<†H†T†^`†$lŽ6ˆD – ’ †®˜<˜10’T®Tˆ ¼U`ŽÈ ™˜yTBx9V’ŠgYwe6Š$ ’e5‰y`” – œ˜l†“Yˆ—[ˆ¢Tap Analysis/Trace, Žfinding the frequency of Œ<a number appearˆ+aft†^ each rollˆ6ˆGdice.Ž@ Now you can†lculate~ˆv probabilitŠxŠOŒ¹ {. [ŒÓŽIn†º is example,R‰“Œù FreqnŽ =Œ11RŽ”550²6†RˆYŒ_Decimal=approx(getright(ans))Œ`Œ**"Š˜0.22 ˆ£ˆ§ ™–U[Œ¼eActDice $2 $0<HT`lx„œ¨´ÀÌØäðü ,8DP\ht€Œ˜¤°¼ÈÔàìø(4@L                                                  aNumber $2 $0<HT`lx„œ¨´ÀÌØäðü ,8DP\ht€Œ˜¤°¼ÈÔàìø(4@L                                 ! " # $ % & ' ( ) * + , - . / 0 1 2n 202000e08 nPr nCr.EAC010000000875É 08 nPr nCr.EAC†Basic Statistics.ACT†*†- ˆ:†>Š Ž Ž$]E †(Œ'[ˆkPermuˆW on and CombinІ#ŠcŽ Ž †¤(10,3)[Œ+=Œ410!Œ 10-3ŒK!ª*Œh7!Žr =10î’9î’8Ž=9†=720 ‡,¸ŒŒË3!î’à˜ˆ5†œ ä¥\î’2‡V =10î’3î’4[ˆŠ12Ž=120\Œ Hint for CASˈ/†D߈J†NXRˆVŒK nPr(10,3)RŽ720š$C¦$1š$Œ^¨N(°FinaForm¸$N†Graph2D†܆& 3Šð ˆLISTSYSˆü†@4ˆ< Modify 0ˆPˆ<STATCALC TˆdˆŒ< \\ˆx SequenceˆŒ,ˆxSheetˆOä|’ŠŒ`’o lveEqˆˆ´†~`wràˆ´(Upˆì’tupFLG1ø(Š<†Lis†{ D‰ˆPic†dÜViewWin†ˆˆŒ_osve†v‡4¤x䉉°Œä’¼ ä’È´ä’ÔÈäŽP à‰ †ä† † ‡^†— ’ø’†¬!’<’P’d(’†u4’ˆ2Š@’†rL’†rX’†rd’ Üp’!ð|† "‘ˆ† #‘”† $‘, † %‘@¬† &‘T¸† '‘hÄ’‰‹І)‘܆ 0*‘¤è¸†ä+†ô†  †,ˆŒ-( †„.<† 0P$† 1d†%†%2x<†3ŒH† 4 T† 5´`† EÈl† F†Ö x’ˆZŠó„†ŽI†Ö† J†Öœ† K†Ö¨† L†Ö´† M†ÖÀ† N†Ö̆ O‘|؆ P†Öä† Q†Öð‡0R‹¸†Öü††Ñ†å S††‡Oˆ˜†]‡[ †A ˆ^†ˆÖ_†(†ˆ´,†a†0†b†4†‰u8’Œ•†D† ͆P†Ά\†‰hh†ׇ¸t’؆€†Ù†Œ†Ú†˜†Û†K¤‘h Financial‡‚Forma†n †ˆ † †ˆŒE‡¥” systemä]listˆŠ^]=’_Œ†`Šaˆ " b~®ÁŽŽž¾ þ@þ€þÀÿÏ@ÁŒ® ÿ@ÿx‡¸°:ŒŽXŠ”XÖ¸Œ»† a†ö seq_h†­b‡FlashBoo‹ ˆ3 ’ ˆÔ’Ó†0’ŠÎ ” —H††‡î<ˆxÒ<ŒÄ ˆˆ †š<‡’“  ö<ö<þxþðÿ,ÿh†<N† ‰ †Œ †ˆo† †0†!@†0PSheet1úÊ»_Š2ž3ž 4†5ž ŒH3DÊ|èš|š†††Š˜| “i™” ™†2††, Š Ž C]E ‰9ŽÀ‰`†$«d«yŽ †j€ « ˆ{†H†6 ††† oŠŽ † `– P2Æ$´$’y– p”x” –<”  ™€–`’ œ0˜ä(1…0qy`ˆä#Y‡uYƒˆH˜–˜œšHª„Æ$ÎH™Œ™˜žˆÊ†v Œ˜ ’ˆQ– Â9ÂZÂ{œ½¶Þ˜Ø¬ð†ˆü †c’e5‰yˆ” – œ™8Vˆ»[Žˆ  Try your own.Ž nPr(12,4) =?\Œ1Ex-1æˆ=æ‰ ‰@N Verify’ RˆnPrŒ 12,4]Œˆ%[Œ$Ž nCr(ˆ%) =?\Œ@Ex-2æˆ(†,æŒ?@NÌCÄeAct010008main.ACT0001020012eActivity Save.EAC010000000875É 08 nPr nCr.EAC†Basic Statistics.ACT†*†- ˆ:†>Š Ž Ž$]E †(Œ'[ˆkPermuˆW on and CombinІ#ŠcŽ Ž †¤(10,3)[Œ+=Œ410!Œ 10-3ŒK!ª*Œh7!Žr =10î’9î’8Ž=9†=720 ‡,¸ŒŒË3!î’à˜ˆ5†œ ä¥\î’2‡V =10î’3î’4[ˆŠ12Ž=120\Œ Hint for CASˈ/†D߈J†NXRˆVŒK nPr(10,3)RŽ720š$C¦$1š$Œ^¨N(°FinaForm¸$N†Graph2D†܆& 3Šð ˆLISTSYSˆü†@4ˆ< Modify 0ˆPˆ<STATCALC TˆdˆŒ< \\ˆx SequenceˆŒ,ˆxSheetˆOä|’ŠŒ`’o lveEqˆˆ´†~`wràˆ´(Upˆì’tupFLG1ø(Š<†Lis†{ D‰ˆPic†dÜViewWin†ˆˆŒ_osve†v‡4¤x䉉°Œä’¼ ä’È´ä’ÔÈäŽP à‰ †ä† † ‡^†— ’ø’†¬!’<’P’d(’†u4’ˆ2Š@’†rL’†rX’†rd’ Üp’!ð|† "‘ˆ† #‘”† $‘, † %‘@¬† &‘T¸† '‘hÄ’‰‹І)‘܆ 0*‘¤è¸†ä+†ô†  †,ˆŒ-( †„.<† 0P$† 1d†%†%2x<†3ŒH† 4 T† 5´`† EÈl† F†Ö x’ˆZŠó„†ŽI†Ö† J†Öœ† K†Ö¨† L†Ö´† M†ÖÀ† N†Ö̆ O‘|؆ P†Öä† Q†Öð‡0R‹¸†Öü††Ñ†å S††‡Oˆ˜†]‡[ †A ˆ^†ˆÖ_†(†ˆ´,†a†0†b†4†‰u8’Œ•†D† ͆P†Ά\†‰hh†ׇ¸t’؆€†Ù†Œ†Ú†˜†Û†K¤‘h Financial‡‚Forma†n †ˆ † †ˆŒE‡¥” systemä]listˆŠ^]=’_Œ†`Šaˆ " b~®ÁŽŽž¾ þ@þ€þÀÿÏ@ÁŒ® ÿ@ÿx‡¸°:ŒŽXŠ”XÖ¸Œ»† a†ö seq_h†­b‡FlashBoo‹ ˆ3 ’ ˆÔ’Ó†0’ŠÎ ” —H††‡î<ˆxÒ<ŒÄ ˆˆ †š<‡’“  ö<ö<þxþðÿ,ÿh†<N† ‰ †Œ †ˆo† †0†!@†0PSheet1úÊ»_Š2ž3ž 4†5ž ŒH3DÊ|èš|š†††Š˜| “i™” ™†2††, Š Ž C]E ‰9ŽÀ‰`†$«d«yŽ †j€ « ˆ{†H†6 ††† oŠŽ † `– P2Æ$´$’y– p”x” –<”  ™€–`’ œ0˜ä(1…0qy`ˆä#Y‡uYƒˆH˜–˜œšHª„Æ$ÎH™Œ™˜žˆÊ†v Œ˜ ’ˆQ– Â9ÂZÂ{œ½¶Þ˜Ø¬ð†ˆü †c’e5‰yˆ” – œ™8Vˆ»[Žˆ  Try your own.Ž nPr(12,4) =?\Œ1Ex-1æˆ=æ‰ ‰@N Verify’ RˆnPrŒ 12,4]Œˆ%[Œ$Ž nCr(ˆ%) =?\Œ@Ex-2æˆ(†,æŒ?@NÌCÄeAct0301da00200008000000001966xœíÜlÔužÇñï÷;ÓS™¶E±ê° Ú_ {ÛÝ”¥ hÁJ‹Ê´·Í•Ri‘²öH7çCív§C—-†3äŽä¼ Ù ¹ð‡»GŒgÈžºä΋?ÖÜ™Ëäâ%æÂCŒÑ{¾óÏ|:8Š?ÖŸÏùt>ß×|Î~g>ßw±_Åì×=ö[Õ¬:ËõAëjøÀðHb·eÉc0nÝoYý;÷Æ÷éH§º¿m˺ûš-+7]•›nr§—_ÌßßhNwܳvMGKÃÜéæïM¯.š¾£hzUÑôÊ¢é–¢éæ¢é¦¢éÆ¢é¢ýk*Ú¿¦¢ýk*Ú¿¦¢ýk*Ú¿¦¢ýk*Ú¿¦¢ýk*Ú¿¦¢ýk,Ú¿Æ¢ýk,Ú¿Æ¢ýk,Ú¿Æ¢ýk,Ú¿Æ¢ýk,Ú¿Æ¢ýûnÑó¿ºhúŽ¢éUEÓ+‹_?EÓÍEÓMEÓz:i¦™fšé?ïôîxÿ 9ݶ¦³ãþ{¶ÜíN;–µ¾0¾~Ï^ù„Qþ‚Ü]¿Ù²’wîõ5µËd¹Z&\•ÏšUVá—A•ulìêîÚÖ¥²ÌÛ¢–Ý´§·ÿájKóÕÌõj¾®î5ÝrX+YŸd•›½,·ìü!Ër¶»Yâ‘}‰Á] ËZ ö%æ.Û—HŒ¸G´à’üÓ™»/¡íx4±î•©}ö—峎ý{%û“Úg;Ÿm’¬ÚÒÙȾ¡õwÊǤê dÑ2/ëè–õW·HÖ^åeý»T6š?¶ûúûïïì•ì¸dKTöОáG{Õê«Ïæ·1Ü×ÿðÈÝnöœ¯ûøeCùg«öB~¾lµÎÞÐYÎÞÒY­Îô±eÃù,¬-»PgA-ÒYήÖY½ÎêtÖ ³Å:kÕÙ5:Û ³kuÖ­³%:ëÑÙu:ÐÙõ:ÕÙ :{\g¥uv£ÎŽël©ÎžÖÙM:;£³zÓÙÍ:{Ag·èìUݪ³¬Î¢:»¨³e:{OgßÉg +u¶\gaÅtÑÙ Åtv›ÎVë¬Agí:kÔY§Îšt¶]gÍ:ëÓY‹ÎFt¶Rgã:[§³I­×Ù¬Î6èì¤Î6êì´ÎîÒÙ3:»[gçuÖ¡³—u¶Igoêl³ÎÞÖÙ=:»¤³Î|¶È¯³{uÒÙ-ÑY—΢:ëÖY‹Îvè¬M~øÝßê¬]gélƒÎztÖ¡³¸Î:u¶SgÝ:›ÑÙz_~¡³^½¨³!½¤³1]ÐYJg¯èlFg¯êì„Î^ÓÙ)½®3ýû4ûG=—Ï‚•¶{>ÜÕW¿LÔy-.¯NÛ X¶#7ª+ç<õús79¶9a•ç¿sçŸ=ý`.ÓÓå2=Ý“Ëôt<—éé¹LyôOG¸å–[n¹ýºßÎ)Aõë}S|¤=>·Ô©vk×­›ok\eåUéžu¥çc{v¾}Êe-–ý/[Vøl#­R½¥éo™s”ëyCÒ"Ò¤µIët¿_7Zcçìé±wÿ·Ü馢鿢関é•EÓ²­¬|ÉÞqEÛ¶ÞòY–±í¹ÓÍEÓ-EÓ+‹¦Ím‹€~úú‹Y¶më·˜í~TÌ?Þmü'–µn~þã÷øÖIÓ߯˜ñ;£ä<¾¹ÏçÜ»ò{'Oï5¥Oi=Ò†¤KKK;!í´´sÒ.H{SÚE¿£4YÞ–åmYÞ–åmYÞ–åmYÞ–åíô'>N|¡|º×côC–£¿¿†ìÏ4O¡oW˜ý¡Âü…~H¿sæöÇ|ãÆúÇ?|~Sy´ñ§ èQyÙMÛíÛö7j=³Æþ˜û6g=e%òÏkžÏK©m}Ý•z¬ yÏÜ×Fxa&±òð÷µ¡û!«Tn®m|`—7¡Æ‚Voµ¬Çݱk½Eû„Ê6®½gó¦u›åïœ0¸Yeƒý#]†eÒ9%¯¸”ʶìÜv÷«E-¯–íJŒìË½Ä«ÔØMŸ›©qå\¦ÆÛÜl$žº¶ªÔXî©\¶ohmç69£ÍsÇFʼl}Ç*›ÉgjO[;6n¾û–{L-ñÁÞ=»#÷Åö%Q‰rNl½=7£ªƒ0—s;àþŒ¸çÁHS{ êö–Ų·Ì.ebÙÆX¶9–m‰eWÆ¢7®x¸±¡aY,šÈ—Žw5`Ù‡­¯9¿¾ævYcS,úãÆ?Î-ï]0Pû7g¹}»wÇ÷D‡sÂýj$=¢†Ò÷ìd¯9˜½)–½‹æÇ×÷ìÏ œ^6¯Ú‡lè`vq,ûÊÁܨPnžõñ]#{ö²õ15†›Ëºã;ìí±l,–]óJs÷­Ý3Ø¿k8²î‘@v{>Ë_‘dïŒe×ŲëcÙ ±ì–X¶+–íŽe7ÌÞ‹ÆWì\Þ$Ç<œx䡾þayt£ù%‹Ÿóµïó«î q¹åd²¬Ì½Ü2¶›¥M†í`*\á]iI…<7÷BKò{>+x)µëS­Aã:Ë’äV»2M…'[Ëç׫ ,êþÂõ•ñd«K–¹O^rBvdÁ)ÙÖX&<1é„¢™pyîzJòŒJqüeiÙ ÷JÊÓÉ Ž:[‡RaûL&Yå“c“Gk…Ìó²´Û¤½)­AÚÛÒ¥]’Ö”îujýÒi–ã© I§Eާv‰tVÊñÔÊSk¯KŸ±kSM“a{½<еmmªíÎF9 Ú¤s—Pm¯tî–ª’£_ÿÄíN­¼BìMr@µ)él–ª‘Î=r@µ'¤Ó)T{J:÷ÊÕž•Î9 Úç¤ÓõÄYuR«½,«ð†À“ ’5~u¥KîÞ!í­ä Ç_%/«½£zÈ{’z¤ýIZÜ;ÊÞ“6“ž´ÃÉ“S“ö/äàÂA‰^”'+¬žì—äØÂõ²ßÿ3ñ_NX=N¯È±…[Õë@Ž-¼A:¯M×ÙáÃKå‘x}:fˬÒû£]x`º»Ìýˆž 'ý©ŠÉ“‹gæW††§2¡C}‡Çågïá1ùÙSsùÈïѽs2ì~J’¯hS•S•O…~y¿íýñ÷Ï}`}ÐöÏ£•ùQ„Ëïü`ôÐÙÊüC‰»­ËVýŸã~w¯¯Jú`<ù»€‹Hþ¾2?1ñ©×íªLÕ_ŸªŸip슣A§bh¦{&è“/G[g‚~õøhO&x¼!]•z¶2ÿi7õB…÷a7ùš˜=šž=þä»ìW?_ÿÒ†'ÿñÉ:síÓ+}ÆŸûE1Y1;ÿôâ7ß?{¶3A;ôë:»çh}Uá#UªnFâ£Áãu³=²ÌV}.ÊfÈ}Þ ¬ŽlJìÞ£ÎÔk6wmZ·i™¾oS¼0²ANsî½äÔ´e›{röîO¬Ù5ˆ®[³ö¡îu›: Ëݙس;1¢–¹sÝ=E÷µ÷?ü°œz#¹Ón´}ݽù ë];Ð?´sO¼W>ýtl4–íÚ›ˆ÷«W|é*,èÝŸ»$$šÖoܬï,õ™ÉýlÈý\š{{lÏ×,™‰ª˜›¨³àR9õ{çÜ}(¹u~ lÞ·;±·W$7õ&Ý)õ®]ö ÷3WSQØ)ïcƒºü­>‹Ôˆ:’_$–ÝqP]¯*,·%1¼o`$ÝËöÌî‹E7ŽìŒ¬ÝÓ›èºìXÕ´_ÞOŽ+^È÷å…µ?Wa©k¡ªNÃö^K*S§¼¼±mu¹Úç^KuôÇûO»-wCÒÌm¹²Ü¡¨ÝçIΓœ'9Oržä<ùež'?͹ëë²Îº/˜{¿éÚ½§ÃFæÕî13ï Ì93ój÷^03¯vïU3ój÷²fæÕî]43¯vï=3ój÷*™W»63¯v/bf^í^Ì̼ڽÕfæÕîµ›™W»×if^íÞv3kÎe}fæÕW»7nf^íÞ¤™yµ{³fæÕî43¯vï´™yµ{Ϙ™W»wÞ̼ڽ—ÍÌ«Ý{Ó̼ڽ·Í̫ݻdfÞu ÿ"#ój÷BfæÕî-1³®\53¯v¯Å̼ë´m‹rï³v¯Ý̼ڽ fÖ“Ë:ÌÌ«ë43¯v¯Û̼ڽÌ}ñj÷zÍÌ«Ý23¯voÌ̼ڽ”™yµ{3fæÕî03¯vï”™yµ{gÍÌ«Ý{ÎÈ®¤vÏ»¾ã7k÷¼_î´ü.¹âš j÷¸å–[n¿Ý·ùsŠœ‡üW»g”î}âÚ=]¸÷)—µXö½¬Wïá~¶©ô^¡9–PPîÍ«îH“¯þ6iò1×ÿç®Ý»‚mAµ{Çúþâ+­ÝóP÷ñ­“V_â1þ(æïŒRóx5Súùœ{ŸÞ»÷§súxöH’6.--í„´ÓÒÎI“éþ7¥]Të¶eyii ÒÚ¤uJë‘6$m\ZÚþälj/V¡ÎÎê1ú¡B]žúLóX…y*ÌþPa~£2Œþ±@¡^OÖ?þáó[†Bíž*ÔîÍc~³o®§¬DþyÍc}NJmëóZÿ—¥Ôceä=s^º.O^…~¨Tn®ÿ~¯£ÆîKìõþŽÜÒ}ÛòÙ[ìÜ¡opíÞò\×ߨkÙ‘:´§×óo1^ÿu¯ÿdãð᪴[Xæþ½·W¸vMG*l¯ž ûÜ2Áä§¼%Õ4þ7†ÑToªÓ'Kª5 *U•jej4W!xÒ­œœW¨ ¥ÖرÔd®@0u#Á¤[x = ‡ô·P­Þ õÕÑÔ[—¶d ÿ¹B›Ìi”–W«¢ÜöÃu…òÀSé7BFy ‹,*|;=jg'þýpS}É­L‡¿[˜ŽÚ5‡Ë&TàTë|«¦ð÷×a¯ °F]Õ_˜q÷Ë^$­Í+ìð ð {½Á!¯@P<õ«‰¿wjÔÕüëÔuU(M]Ë¿Ašº”¯JÕ•ü¥© ùK¥]P¥ÒÔ•ûzuå^zéo™î³k=6¥ ÇœÚ`&|8ùÄ»öð]“ª2ð¤]›<äº×T!`mƒ.\.kP×ècª*!“+ ìö {dwÿrâGNí€W8ª*¥=® ¥¥½Çà¸* ”ö´ªvȸåœöziçdÿöD…S«*'7fr•“wer•“w{Å^qÁ¦é>'\é–9Œ9á°[æv·Ìá¤-G%Çso®ª!¼ZW5lñªÂªŽ²KÍìÁv¯Ê¡/¹µPå0àU9 yU#^•èWå0æ=kãòМœÛ‰ôyga½[úð†³ð|æŒý‹ôEg¡*|qÚï,Tµ“/M×9 Uùą阳PÕK¼2Ýæ,ò»•Ý΢[ùÐç,RÕ“¯ËÁ-R¯Ÿ?ÊÁ-j™>4‡¬o½jîˆu²"5¯Ìýu½Yž1êÆ™ùé s¨9Õ0¿\S¬ÛV{ÿ®Dªá*óâŽï ÙM†3!»ÇýW?ýò;ëàÔOœþgçÖ8üÖª|6÷{¡ÿ£Š¬âåòwWx÷NT÷ž}ëR®<¢Â-8ôƒ@¾²yg2X¹9±ýžÞÄ[Sͪ<âª9_x’ ™P™{3‘_¦m;YžôWX~÷ˆ“­eꈭ§Zkv|îaÙ…JU3áXvzI¥»&Ù^:æWÉ;­nÑÄÅbôýÃÉÚ¢¿S3fBî6-+)ϯ¯Âû“8õÖ±æXLÞ2ûð‹jý'huïÖX¿zýAkâ²ò yl&78Íí¿óÉwÕ'Çž %6;¦N#ÕnéD¹[:áz쉻}Ò™¨ššŸªL.)ÿ+÷ëèáÄÔ¹Ã=¹º‰¿í5êf‚ú°ƒ¿¹Íöeêó5É5UªŠb*h÷ úUE:å„ìçëÏÔgþà ©º Ÿ¿½mêËÇ*ªelûèã•ûoi¼ÿð‡ªý_:=3O;ö}3ݳ Çþ¢PE‘ÍWQÚ–¯¢µË~]÷|}ꜷo¾U6U• Ê*ƒ¾rËŸ f®ÎDNÖž¾y¶{vàÝ­ïfÞùƒ]5yáPÔ+©´ë½·UÚiÝÒz¤ ëðÙ[ï;2äsªkŽŒùœ‡ûޤ|¾¥õGf|¾ýãGNøüÍ«ŽœòùS™#g+ÊÚ7äö ,d¹Û-Sãq¶üf÷̖ꊩU©v;p4˜™—”ã±­ÙÖÙFÇnÈt;r|Ý©ég|e[{¦Î;c³*œîŽ~÷¾ÌD]…mÿhÛþΉú ùÇ'º6D]©Úæ¾|?Ëùß»l J«“&gÔÌj•&ê–Ö#M¶•ö¸´´´ãª_ÚUz/íi¯JËæþ¤Ð{ÒäwT(,-"-&mµ´viÒ¶Kë“6"m\Ú¤´Yi'¥–öŒ´óÒ^–ö¦´·¥]’&¯Ì|a -‘•Ö"­MZ‡£ŽÁ‡q_-^ß6úŽÑ÷•ÈËKôí¹¹­²+Øn©¾¯Ä:Kíg©}.»‚ý±K¬¿¬Ä>”:öRƒS"//1O©c,µŸ¥æ)+1ÿ•<ž¥ûú¹’÷E©×¶ù