Question Number 111906 by mr W last updated on 05/Sep/20 Answered by PRITHWISH SEN 2 last updated on 22/Sep/20 $$\mathrm{Disarrangement}\:\mathrm{of}\:\mathrm{6}\:\mathrm{cards}\:!\mathrm{6}=\mathrm{265} \\ $$$$\mathrm{now}\:\mathrm{in}\:\mathrm{this}\:\mathrm{265}\:\mathrm{ways}\:\mathrm{card}\:\mathrm{no}.\:\mathrm{1}\:\mathrm{can}\:\mathrm{be}\:\mathrm{in}\: \\ $$$$\mathrm{envelope}\:\mathrm{no}.\:\mathrm{2},\mathrm{3},\mathrm{4},\mathrm{5}\:\mathrm{or}\:\mathrm{6}\:\mathrm{and}\:\mathrm{in}\:\mathrm{each}\:\mathrm{case}\:\mathrm{the} \\…
Question Number 177309 by SLVR last updated on 03/Oct/22 $${How}\:{many}\:\mathrm{3}\:{digited}\:{numbers}\: \\ $$$$\left.{which}\:{are}\:{divisible}\:{by}\:\mathrm{1}\right)\mathrm{3} \\ $$$$\left.\mathrm{2}\left.\right)\left.\mathrm{4}\left.\:\left.\:\left.\:\:\mathrm{3}\right)\mathrm{5}\:\:\:\:\mathrm{4}\right)\mathrm{6}\:\:\:\mathrm{5}\right)\mathrm{7}\:\:\:\:\mathrm{6}\right)\mathrm{8}\:\:\mathrm{7}\right)\mathrm{9} \\ $$$${with}\:{repetetion}\:{of}\:{digits}\:{is} \\ $$$${NOT}\:{allowed}…{one}\:{problem}\:{process} \\ $$ Commented by SLVR last updated…
Question Number 111732 by Aina Samuel Temidayo last updated on 04/Sep/20 $$\mathrm{A}\:\mathrm{blind}\:\mathrm{man}\:\mathrm{is}\:\mathrm{to}\:\mathrm{place}\:\mathrm{5}\:\mathrm{letters}\:\mathrm{into}\:\mathrm{5} \\ $$$$\mathrm{pigeon}\:\mathrm{holes},\:\mathrm{how}\:\mathrm{many}\:\mathrm{ways}\:\mathrm{can}\:\mathrm{4}\:\mathrm{of} \\ $$$$\mathrm{the}\:\mathrm{letters}\:\mathrm{be}\:\mathrm{wrongly}\:\mathrm{placed}? \\ $$$$\left(\mathrm{note}\:\mathrm{that}\:\mathrm{only}\:\mathrm{one}\:\mathrm{letter}\:\mathrm{must}\:\mathrm{be}\:\mathrm{in}\:\mathrm{a}\right. \\ $$$$\left.\mathrm{pigeon}\:\mathrm{hole}\right) \\ $$ Answered by mr…
Question Number 46143 by aseerimad last updated on 21/Oct/18 Answered by tanmay.chaudhury50@gmail.com last updated on 22/Oct/18 $$\mathrm{52}{C}_{\mathrm{26}} ×\mathrm{26}{C}_{\mathrm{26}} \\ $$$$=\frac{\mathrm{52}!}{\mathrm{26}!\mathrm{26}!} \\ $$ Commented by aseerimad…
Question Number 177040 by cortano1 last updated on 30/Sep/22 Answered by mr W last updated on 30/Sep/22 $${total}\:{number}\:{of}\:\mathrm{9}−{digit}\:{numbers}\:{is}: \\ $$$$\mathrm{9}!=\mathrm{362880} \\ $$$$ \\ $$$${number}\:{of}\:{those}\:{which}\:{are}\:{divisible} \\…
Question Number 177008 by Ar Brandon last updated on 29/Sep/22 Answered by Rasheed.Sindhi last updated on 29/Sep/22 $${Let}\:{t}\:{is}\:{total}\:{of}\:{card}\:{numbers}\:{chose}\:{by}\:{players}. \\ $$$${Efe}'{s}\:{card}\:{number}=\mathrm{3} \\ $$$$\:\:\:\:\:\:\:\mathrm{6}\leqslant{t}\leqslant\mathrm{20} \\ $$$${If}\:{t}\in\mathbb{P}\:{then}\:{possible}\:{values}\:{for}\:{t}: \\…
Question Number 177007 by Ar Brandon last updated on 29/Sep/22 Answered by mr W last updated on 29/Sep/22 $$\mathrm{1}.\:{he}\:{buys}\:{the}\:\mathrm{13}^{{th}} \:{floor}: \\ $$$$\mathrm{12}^{{th}} \:{floor}\:{is}\:{also}\:{bought}.\:{to}\:{buy}\:{the}\: \\ $$$${rest}\:\mathrm{6}\:{floors}\:{there}\:{are}\:{C}_{\mathrm{6}}…
Question Number 111394 by Aina Samuel Temidayo last updated on 03/Sep/20 $$\mathrm{A}\:\mathrm{teacher}\:\mathrm{conducts}\:\mathrm{a}\:\mathrm{test}\:\mathrm{for}\:\mathrm{five} \\ $$$$\mathrm{students}.\:\mathrm{He}\:\mathrm{provides}\:\mathrm{the}\:\mathrm{marking} \\ $$$$\mathrm{scheme}\:\mathrm{and}\:\mathrm{asked}\:\mathrm{them}\:\mathrm{to}\:\mathrm{exchange} \\ $$$$\mathrm{their}\:\mathrm{scripts}\:\mathrm{such}\:\mathrm{that}\:\mathrm{none}\:\mathrm{of}\:\mathrm{them} \\ $$$$\mathrm{marks}\:\mathrm{his}\:\mathrm{own}\:\mathrm{script}.\:\mathrm{How}\:\mathrm{many}\:\mathrm{ways} \\ $$$$\mathrm{can}\:\mathrm{the}\:\mathrm{students}\:\mathrm{carry}\:\mathrm{out}\:\mathrm{the} \\ $$$$\mathrm{marking}? \\…
Question Number 111393 by Aina Samuel Temidayo last updated on 03/Sep/20 $$\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{the}\:\mathrm{coefficients}\:\mathrm{in}\:\mathrm{the} \\ $$$$\mathrm{expansion}\:\mathrm{of}\:\left(\mathrm{2015v}−\mathrm{2015u}+\mathrm{1}\right)^{\mathrm{2015}} ? \\ $$ Commented by mr W last updated on 03/Sep/20…
Question Number 111275 by Aina Samuel Temidayo last updated on 03/Sep/20 $$\mathrm{In}\:\mathrm{a}\:\mathrm{tennis}\:\mathrm{tournament}\:\mathrm{n}\:\mathrm{women}\:\mathrm{and} \\ $$$$\mathrm{2n}\:\mathrm{men}\:\mathrm{played}.\:\mathrm{Each}\:\mathrm{player}\:\mathrm{played} \\ $$$$\mathrm{exactly}\:\mathrm{one}\:\mathrm{match}\:\mathrm{with}\:\mathrm{every}\:\mathrm{other} \\ $$$$\mathrm{player}.\:\mathrm{If}\:\mathrm{there}\:\mathrm{are}\:\mathrm{no}\:\mathrm{ties}\:\mathrm{and}\:\mathrm{the} \\ $$$$\mathrm{number}\:\mathrm{of}\:\mathrm{the}\:\mathrm{matches}\:\mathrm{won}\:\mathrm{by}\:\mathrm{women} \\ $$$$\mathrm{to}\:\mathrm{the}\:\mathrm{number}\:\mathrm{of}\:\mathrm{matches}\:\mathrm{won}\:\mathrm{by}\:\mathrm{men} \\ $$$$\mathrm{is}\:\mathrm{7}:\mathrm{5},\:\mathrm{find}\:\mathrm{n}. \\…