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…
Question Number 124709 by benjo_mathlover last updated on 05/Dec/20 $${Between}\:\mathrm{20000}\:{and}\:\mathrm{70000}\: \\ $$$${find}\:{the}\:{number}\:{of}\:{even}\:{integers} \\ $$$${in}\:{which}\:{no}\:{digits}\:{is}\:{repeated} \\ $$ Answered by liberty last updated on 05/Dec/20 $${Let}\:{abcde}\:{be}\:{a}\:{required}\:{even}\:{integer}.\: \\…
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Question Number 59021 by mr W last updated on 03/May/19 $$\left[{Q}\mathrm{58885}\:{reposted}\right] \\ $$$${How}\:{many}\:\mathrm{4}−{digit}\:{numbers}\:{abcd}\:{exist} \\ $$$${which}\:{are}\:{divisible}\:{by}\:\mathrm{3}\:{and}\:{satisfy} \\ $$$${a}\leqslant{b}\leqslant{c}\leqslant{d}? \\ $$ Commented by tanmay last updated on…