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…
Question Number 85817 by jagoll last updated on 25/Mar/20 $$\mathrm{what}\:\mathrm{is}\:\mathrm{coefficient}\:\mathrm{of}\:\mathrm{x}^{\mathrm{2}} \:\mathrm{in}\: \\ $$$$\mathrm{the}\:\mathrm{expansion}\:\left[\:\left(\mathrm{1}−\mathrm{x}\right)\left(\mathrm{1}+\mathrm{2x}\right)\right]^{\mathrm{6}} \\ $$ Answered by john santu last updated on 25/Mar/20 $$\left(\mathrm{1}+{x}−\mathrm{2}{x}^{\mathrm{2}} \right)^{\mathrm{6}\:\:}…
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Question Number 85187 by mathocean1 last updated on 19/Mar/20 $${Show}\:{that}\:\forall\:{n},\:{p}\:\in\:\mathbb{N}^{\ast\:} \\ $$$${C}_{{n}−\mathrm{1}} ^{\:{p}−\mathrm{1}} +{C}_{{n}−\mathrm{1}} ^{\:{p}} ={C}_{{n}} ^{\:{p}} \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 150554 by pete last updated on 13/Aug/21 $$\mathrm{Show}\:\mathrm{that}\:\mathrm{n}_{\mathrm{C}_{\mathrm{r}} } =\frac{\mathrm{n}\left(\mathrm{n}−\mathrm{1}\right)\left(\mathrm{n}−\mathrm{2}\right)…\left(\mathrm{n}−\mathrm{r}+\mathrm{1}\right)}{\mathrm{r}!} \\ $$ Answered by Ar Brandon last updated on 13/Aug/21 $$\frac{{n}\left({n}−\mathrm{1}\right)\left({n}−\mathrm{2}\right)…\left({n}−{r}+\mathrm{1}\right)}{{r}!} \\ $$$$=\frac{{n}\left({n}−\mathrm{1}\right)…\left({n}−{r}+\mathrm{1}\right)\left({n}−{r}\right)!}{\left({n}−{r}\right)!{r}!}…
Question Number 84998 by jagoll last updated on 18/Mar/20 $$\mathrm{what}\:\mathrm{is}\:\mathrm{coefficient}\:\mathrm{of}\:\mathrm{x}^{\mathrm{29}} \\ $$$$\mathrm{in}\:\mathrm{expression}\:\left(\mathrm{1}+\mathrm{x}^{\mathrm{5}} +\mathrm{x}^{\mathrm{7}} +\mathrm{x}^{\mathrm{9}} \right)^{\mathrm{29}} \\ $$ Answered by mind is power last updated on…
Question Number 84993 by mr W last updated on 18/Mar/20 $$\mathrm{100}\:{apples}\:{should}\:{be}\:{packed}\:{in}\:{three} \\ $$$${boxes}\:{and}\:{each}\:{box}\:{should}\:{contain} \\ $$$${at}\:{least}\:\mathrm{10}\:{apples}.\:{in}\:{how}\:{many}\:{ways} \\ $$$${can}\:{this}\:{be}\:{done}? \\ $$ Commented by john santu last updated…