Question Number 198548 by HomeAlone last updated on 21/Oct/23 $${return}\mathrm{return}\left(\right) \\ $$$$\mathrm{p}<\mathrm{1} \\ $$$$\mathrm{p} \\ $$$$\mathrm{2} \\ $$$$\mathrm{3} \\ $$$$\mathrm{4} \\ $$$$\mathrm{5} \\ $$$$\mathrm{6} \\…
Question Number 198283 by cortano12 last updated on 16/Oct/23 $$\mathrm{Given}\:\mathrm{the}\:\mathrm{number}\:\mathrm{of}\:\:\mathrm{consisting} \\ $$$$\:\mathrm{of}\:\mathrm{4}\:\mathrm{digits}\:\mathrm{abcd}\:\mathrm{such}\:\mathrm{that}\: \\ $$$$\:\mathrm{a}\leqslant\mathrm{b}\leqslant\mathrm{c}\leqslant\mathrm{d}\:\mathrm{is}\:… \\ $$$$\:\left(\mathrm{A}\right)\:\mathrm{495}\:\:\:\left(\mathrm{B}\right)\:\mathrm{385}\:\:\:\:\:\left(\mathrm{C}\right)\:\mathrm{275} \\ $$$$\:\left(\mathrm{D}\right)\:\mathrm{165}\:\:\:\:\left(\mathrm{E}\right)\:\mathrm{55}\: \\ $$ Commented by mr W last…
Question Number 198242 by Tawa11 last updated on 15/Oct/23 How many numbers with a maximum of 5 digits, greater than 4000, can be formed with…
Question Number 198231 by pticantor last updated on 14/Oct/23 Answered by witcher3 last updated on 14/Oct/23 $$\mathrm{C}_{\mathrm{n}} ^{\mathrm{p}} =\frac{\mathrm{n}!}{\mathrm{p}!.\left(\mathrm{n}−\mathrm{p}\right)!} \\ $$$$\mathrm{pC}_{\mathrm{n}} ^{\mathrm{p}} =\frac{\mathrm{n}!}{\left(\mathrm{p}−\mathrm{1}\right)!.\left(\mathrm{n}−\mathrm{p}\right)!}=\mathrm{n}.\frac{\left(\mathrm{n}−\mathrm{1}\right)!}{\left(\mathrm{p}−\mathrm{1}\right)!.\left(\mathrm{n}−\mathrm{1}−\left(\mathrm{p}−\mathrm{1}\right)\right)!} \\ $$$$=\mathrm{nC}_{\mathrm{n}−\mathrm{1}}…
Question Number 198022 by cortano12 last updated on 08/Oct/23 $$\:\:\mathrm{Five}\:\mathrm{letters}\:\mathrm{are}\:\mathrm{selected}\:\mathrm{from} \\ $$ Answered by mr W last updated on 08/Oct/23 $${OOOXX}\:\:\Rightarrow\mathrm{2} \\ $$$${OOOXY}\:\:\Rightarrow\mathrm{2}×{C}_{\mathrm{2}} ^{\mathrm{4}} =\mathrm{12}…
Question Number 197589 by mr W last updated on 23/Sep/23 $${how}\:{many}\:{natural}\:{numbers}\:{with}\:\mathrm{4} \\ $$$${different}\:{digits}\:{are}\:{divisible}\:{by}\:\mathrm{3}? \\ $$ Answered by mr W last updated on 24/Sep/23 $${A}=\left\{\mathrm{1},\mathrm{4},\mathrm{7}\right\} \\…
Question Number 197578 by mr W last updated on 22/Sep/23 Commented by mr W last updated on 22/Sep/23 $${unsolved}\:{old}\:{question}\:{Q}#\mathrm{196915} \\ $$ Answered by mr W…
Question Number 197564 by SLVR last updated on 21/Sep/23 $${sir}…{number}\:{of}\:\mathrm{3}\:{digit} \\ $$$${numbers}\:{which}\:{are}\:{divisible} \\ $$$${by}\: \\ $$$$\left.{a}\left.\right)\left.\mathrm{3}\left.\:\left.\:\left.{b}\left.\right)\mathrm{4}\:\:{c}\right)\mathrm{6}\:\:{d}\right)\mathrm{7}\:\:{e}\right)\mathrm{8}\:\:{f}\right)\mathrm{9}\:\:{g}\right)\mathrm{11} \\ $$$${when}\:{repetetion}\:{is} \\ $$$$\left.\mathrm{1}\left.\right){Allowwd}\:\:\mathrm{2}\right){Not}\:{allowed}.. \\ $$$${kindly}\:{help}\:{me}\:{sir} \\ $$ Commented…
Question Number 197311 by cortano12 last updated on 13/Sep/23 $$\:\:\:\:\:\mathrm{Prove}\:\mathrm{that}\: \\ $$$$\:\:\:\:\:\:_{\mathrm{n}+\mathrm{1}} \:\mathrm{C}_{\mathrm{r}} \:=\:_{\mathrm{n}} \mathrm{C}_{\mathrm{r}} \:+\:_{\mathrm{n}} \mathrm{C}_{\mathrm{r}−\mathrm{1}} \: \\ $$ Answered by qaz last updated…
Question Number 196322 by sniper237 last updated on 22/Aug/23 $$\:\:\:\:{f}^{\left(\mathrm{1}/\mathrm{2}\right)} \left({x}\right)=\:\frac{{d}}{{dx}}\left(\int_{\mathrm{0}} ^{{x}} \:\frac{{f}\left({x}−{t}\right)}{\:\sqrt{\pi{t}}}{dt}\right) \\ $$$${Prove}\:\:{that}\:\:\:\:\left({f}^{\left(\mathrm{1}/\mathrm{2}\right)} \right)^{\left(\mathrm{1}/\mathrm{2}\right)} =\:{f}\:'\:\:\:\: \\ $$$${At}\:\:{least}\:\:{for}\:\:{f}\:=\:\:\mathrm{1}\:\:{then}\:\:{f}\:=\:{x} \\ $$ Answered by witcher3 last…