Question Number 59625 by Tawa1 last updated on 12/May/19 $$\mathrm{Sum}\:\mathrm{the}\:\mathrm{series}:\:\:\:\:\:\:\:\left(\frac{\overset{\boldsymbol{\mathrm{n}}} {\:}\boldsymbol{\mathrm{C}}_{\mathrm{1}} }{\overset{\boldsymbol{\mathrm{n}}} {\:}\boldsymbol{\mathrm{C}}_{\mathrm{0}} }\right)^{\mathrm{2}} \:+\:\left(\mathrm{2}\:×\:\frac{\overset{\boldsymbol{\mathrm{n}}} {\:}\boldsymbol{\mathrm{C}}_{\mathrm{2}} }{\overset{\boldsymbol{\mathrm{n}}} {\:}\boldsymbol{\mathrm{C}}_{\mathrm{1}} }\right)\:+\:\left(\mathrm{3}\:×\:\frac{\overset{\boldsymbol{\mathrm{n}}} {\:}\boldsymbol{\mathrm{C}}_{\mathrm{3}} }{\overset{\boldsymbol{\mathrm{n}}} {\:}\boldsymbol{\mathrm{C}}_{\mathrm{2}} }\right)^{\mathrm{2}} \:+\:….\:\:\boldsymbol{\mathrm{n}}\:\mathrm{terms} \\…
Question Number 190602 by uchihayahia last updated on 07/Apr/23 $$ \\ $$$$\: \\ $$$$\:{let}\:{S}=\left\{{a},{b},{c},{d},{e},{f}\right\} \\ $$$$\:{if}\:{we}\:{take}\:{any}\:{subset}\:{S}\:\left({same}\:{subset}\:{is}\:{allowed}\right), \\ $$$$\:{it}\:{also}\:{can}\:{be}\:{S},\:{which}\:{will}\:{form}\:{S}\:{if}\:{we}\:{join}\:{them}, \\ $$$${order}\:{of}\:{operation}\:{does}\:{not}\:{matter} \\ $$$$\:\left(\left\{{a},{b},{c},{d}\right\},\left\{{d},{e},{f}\right\}\right)\:{is}\:{the}\:{same}\:{as} \\ $$$$\:\left(\left\{{d},{e},{f}\right\},\left\{{a},{b},{c},{d}\right\}\right) \\…
Question Number 124916 by liberty last updated on 07/Dec/20 $${The}\:{number}\:{of}\:{ways}\:{arrangements}\: \\ $$$${of}\:{the}\:{word}\:'{MASKARA}'\:{with}\:{exactly} \\ $$$$\mathrm{2}\:{A}'{s}\:\:{are}\:{adjacent}??\: \\ $$ Answered by mr W last updated on 07/Dec/20 $$\_\mathrm{M\_S\_K\_R\_}…
Question Number 124878 by mr W last updated on 06/Dec/20 $$\mathrm{20}\:{students}\:{should}\:{stand}\:{in}\:\mathrm{5} \\ $$$${different}\:{rows}.\:{each}\:{row}\:{should}\:{have} \\ $$$${at}\:{least}\:\mathrm{2}\:{students}.\:{in}\:{how}\:{many}\:{ways} \\ $$$${can}\:{you}\:{arrange}\:{them}? \\ $$ Answered by liberty last updated on…
Question Number 124826 by bramlexs22 last updated on 06/Dec/20 $$\:{How}\:{many}\:{ways}\:{are}\:{there}\:{to}\:{arrange}\: \\ $$$${the}\:{letters}\:{of}\:{the}\:{word}\:'\:{VISITING}' \\ $$$${if}\:{no}\:{two}\:{I}'{s}\:{are}\:{adjacent}\:? \\ $$ Answered by mr W last updated on 06/Dec/20 $${Method}\:{I}…
Question Number 124829 by bramlexs22 last updated on 06/Dec/20 $$\:{How}\:{many}\:{ways}\:{are}\:{there}\:{to}\:{arrange} \\ $$$${the}\:{letters}\:{of}\:{the}\:{word}\:'{ALAMATAR}'\:{if} \\ $$$${no}\:{two}\:{A}'{s}\:{are}\:{adjacent}?\: \\ $$ Answered by mr W last updated on 06/Dec/20 $${to}\:{arrange}\:{at}\:{first}\:{the}\:{four}\:{letters}…
Question Number 190347 by mustafazaheen last updated on 01/Apr/23 $${how}\:{is}\:{solution} \\ $$$$\underset{{x}\rightarrow\mathrm{sin}\pi\:} {\mathrm{lim}}\frac{\mathrm{sin}\frac{\pi}{\mathrm{2}}}{\mathrm{sin}{x}}=? \\ $$ Answered by JDamian last updated on 01/Apr/23 $${L}=\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{1}}{\mathrm{sin}\:{x}}\:=\:\begin{cases}{+\infty\:\:\:{x}\rightarrow\mathrm{0}^{+} }\\{−\infty\:\:{x}\rightarrow\mathrm{0}^{−}…
Question Number 124806 by bramlexs22 last updated on 06/Dec/20 Answered by mr W last updated on 06/Dec/20 $$\left({i}\right) \\ $$$$\mathrm{6}=\mathrm{1}+\mathrm{5}=\mathrm{2}+\mathrm{4}=\mathrm{3}+\mathrm{3} \\ $$$$\Rightarrow{C}_{\mathrm{1}} ^{\mathrm{6}} ×\mathrm{4}!+{C}_{\mathrm{2}} ^{\mathrm{6}}…
Question Number 190260 by alcohol last updated on 30/Mar/23 $${f}\::\:\left[\mathrm{1},\:\mathrm{3}\right]\:\rightarrow\mathbb{R}\:,\:{f}\left({x}\right)\:=\:\frac{\mathrm{1}}{{x}} \\ $$$${A}\left(\mathrm{1},\:\mathrm{1}\right) \\ $$$${B}\left(\mathrm{1},\:\frac{\mathrm{1}}{\mathrm{3}}\right) \\ $$$${B}'\left({b},\:\frac{\mathrm{1}}{{b}}\right)\:,\:{b}\:\geqslant\:\mathrm{1} \\ $$$${Find} \\ $$$${i}.\:{equation}\:{of}\:{line}\:{AB}' \\ $$$${ii}.\:{equation}\:{of}\:{tangent}\:{T}\:'\:{to}\:{C}_{{f}} \:{at}\:{point} \\ $$$${with}\:{x}\:=\:\frac{\mathrm{1}\:+\:{b}}{\mathrm{2}}…
Question Number 124712 by benjo_mathlover last updated on 05/Dec/20 $${In}\:{how}\:{many}\:{ways}\:\:{can}\:\mathrm{5}\:{boys}\:{and}\:\mathrm{3}\:{girls} \\ $$$${be}\:{seated}\:{around}\:{a}\:{table}\:{if}\: \\ $$$$\left({i}\right)\:{boy}\:{B}_{\mathrm{3}} \:{and}\:{G}_{\mathrm{2}} \:{are}\:{not}\:{adjacent} \\ $$$$\left({ii}\right)\:{no}\:{girls}\:{are}\:{adjacent}\: \\ $$ Answered by liberty last updated…