Question Number 21406 by Tinkutara last updated on 23/Sep/17 $$\mathrm{Find}\:\mathrm{the}\:\mathrm{number}\:\mathrm{of}\:\mathrm{ways}\:\mathrm{in}\:\mathrm{which}\:{n} \\ $$$$\mathrm{distinct}\:\mathrm{balls}\:\mathrm{can}\:\mathrm{be}\:\mathrm{put}\:\mathrm{into}\:\mathrm{three} \\ $$$$\mathrm{boxes}\:\mathrm{so}\:\mathrm{that}\:\mathrm{no}\:\mathrm{two}\:\mathrm{boxes}\:\mathrm{remain} \\ $$$$\mathrm{empty}. \\ $$ Commented by mrW1 last updated on 06/Oct/17…
Question Number 21404 by Tinkutara last updated on 23/Sep/17 $$\mathrm{Prove}\:\mathrm{that}\:\left(\mathrm{6}{n}\right)!\:\mathrm{is}\:\mathrm{divisible}\:\mathrm{by}\:\mathrm{2}^{\mathrm{2}{n}} .\mathrm{3}^{{n}} . \\ $$ Answered by dioph last updated on 23/Sep/17 $$\mathrm{if}\:{n}\:>\:\mathrm{1},\:\mathrm{there}\:\mathrm{are}\:\mathrm{at}\:\mathrm{least}\:\mathrm{3}{n}\:\mathrm{even} \\ $$$$\mathrm{numbers}\:\mathrm{and}\:\mathrm{2}{n}\:\mathrm{multiples}\:\mathrm{of}\:\mathrm{3}\:\mathrm{in} \\…
Question Number 21374 by Tinkutara last updated on 22/Sep/17 $$\mathrm{In}\:\mathrm{how}\:\mathrm{many}\:\mathrm{ways}\:\mathrm{can}\:\mathrm{the}\:\mathrm{letters}\:\mathrm{of}\:\mathrm{the} \\ $$$$\mathrm{word}\:\mathrm{PATLIPUTRA}\:\mathrm{be}\:\mathrm{arranged},\:\mathrm{so} \\ $$$$\mathrm{that}\:\mathrm{the}\:\mathrm{relative}\:\mathrm{order}\:\mathrm{of}\:\mathrm{vowels}\:\mathrm{are} \\ $$$$\mathrm{consonants}\:\mathrm{do}\:\mathrm{not}\:\mathrm{alter}? \\ $$ Commented by mrW1 last updated on 22/Sep/17…
Question Number 86684 by john santu last updated on 30/Mar/20 $$\mathrm{If}\:\left(\mathrm{1}+\mathrm{px}+\mathrm{qx}^{\mathrm{2}} \right)^{\mathrm{8}} \:=\:\mathrm{1}+\mathrm{8x}+\mathrm{52x}^{\mathrm{2}} +\mathrm{kx}^{\mathrm{3}} +… \\ $$$$\mathrm{find}\:\mathrm{p}\:,\:\mathrm{q}\:\mathrm{and}\:\mathrm{k}.\: \\ $$ Answered by jagoll last updated on…
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Question Number 151832 by DELETED last updated on 23/Aug/21 Answered by DELETED last updated on 23/Aug/21 $$\left.\mathrm{57}\right).\:\mathrm{R}_{\mathrm{s}} =\mathrm{2R}+\mathrm{2R}=\mathrm{4R} \\ $$$$\:\:\:\:\:\:\:\:\:\:\frac{\mathrm{1}}{\mathrm{R}_{\mathrm{p}} }=\frac{\mathrm{1}}{\mathrm{2R}}+\frac{\mathrm{1}}{\mathrm{4R}}=\frac{\mathrm{3}}{\mathrm{4R}} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\mathrm{R}_{\mathrm{p}} =\frac{\mathrm{4R}}{\mathrm{3}}\: \\…
Question Number 151828 by DELETED last updated on 23/Aug/21 Answered by DELETED last updated on 23/Aug/21 $$\mathrm{R}_{\mathrm{s1}} =\mathrm{10}\Omega+\mathrm{10}\Omega=\mathrm{20}\Omega \\ $$$$\mathrm{R}_{\mathrm{s2}} =\mathrm{10}\Omega+\mathrm{10}\Omega=\mathrm{20}\Omega \\ $$$$\frac{\mathrm{1}}{\mathrm{R}_{\mathrm{p}} }=\frac{\mathrm{1}}{\mathrm{R}_{\mathrm{s1}} }\:+\frac{\mathrm{1}}{\mathrm{R}_{\mathrm{s2}}…
Question Number 151823 by DELETED last updated on 23/Aug/21 Answered by DELETED last updated on 23/Aug/21 $$\mathrm{54}.\:\:\mathrm{R}_{\mathrm{1}} :\mathrm{R}_{\mathrm{2}} =\rho\frac{\mathrm{l}_{\mathrm{1}} }{\pi\mathrm{R}_{\mathrm{1}} ^{\mathrm{2}} }:\rho\frac{\mathrm{l}_{\mathrm{2}} }{\pi\mathrm{R}_{\mathrm{2}} ^{\mathrm{2}} }…
Question Number 151615 by pete last updated on 22/Aug/21 $$\mathrm{How}\:\mathrm{many}\:\mathrm{numbers}\:\mathrm{greater}\:\mathrm{than}\:\mathrm{200}\:\mathrm{can} \\ $$$$\mathrm{be}\:\mathrm{formed}\:\mathrm{from}\:\mathrm{the}\:\mathrm{digits}\:\mathrm{1},\mathrm{2},\mathrm{3},\mathrm{4},\mathrm{5}\:\mathrm{if}\:\mathrm{no} \\ $$$$\mathrm{digit}\:\mathrm{is}\:\mathrm{to}\:\mathrm{be}\:\mathrm{repeated}\:\mathrm{in}\:\mathrm{any}\:\mathrm{particular} \\ $$$$\mathrm{number}? \\ $$$$ \\ $$ Answered by mr W last…
Question Number 151485 by liberty last updated on 21/Aug/21 Answered by iloveisrael last updated on 21/Aug/21 $$\:{N}\left({A}\right)=\:\frac{\mathrm{5}!}{\mathrm{3}!}×\frac{\mathrm{7}!}{\mathrm{2}!}\:=\:\frac{\mathrm{120}}{\mathrm{6}}\:×\frac{\mathrm{5040}}{\mathrm{2}} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:=\:\mathrm{20}×\mathrm{2520}=\mathrm{50400} \\ $$ Terms of Service Privacy…