Question Number 107844 by mr W last updated on 13/Aug/20 $${A}\:{general}\:{case}: \\ $$$${we}\:{have}\:{totally}\:{n}\:{letters},\:{among}\:{them} \\ $$$${n}_{\mathrm{1}} \:{times}\:{A},\:{n}_{\mathrm{2}} \:{times}\:{B},\:{n}_{\mathrm{3}} \:{times}\:{C}, \\ $$$${n}_{\mathrm{4}} \:{times}\:{D}\:{etc}. \\ $$$$\left({n}_{\mathrm{1}} ,{n}_{\mathrm{2}} ,{n}_{\mathrm{3}}…
Question Number 173354 by pete last updated on 10/Jul/22 $$\mathrm{A}\:\mathrm{three}−\mathrm{digit}\:\mathrm{odd}\:\mathrm{number}\:\mathrm{less}\:\mathrm{than}\:\mathrm{500} \\ $$$$\mathrm{is}\:\mathrm{to}\:\mathrm{be}\:\mathrm{formed}\:\mathrm{from}\:\mathrm{1},\mathrm{2},\mathrm{3},\mathrm{4}\:\mathrm{and}\:\mathrm{5}.\:\mathrm{If}\:\mathrm{repetition} \\ $$$$\mathrm{of}\:\mathrm{digits}\:\mathrm{is}\:\mathrm{allowed},\:\mathrm{in}\:\mathrm{how}\:\mathrm{many}\:\mathrm{ways} \\ $$$$\mathrm{can}\:\mathrm{this}\:\mathrm{be}\:\mathrm{done}? \\ $$ Commented by pete last updated on 10/Jul/22…
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Question Number 42110 by rahul 19 last updated on 18/Aug/18 Commented by Tawa1 last updated on 19/Aug/18 $$\mathrm{sweet} \\ $$ Answered by tanmay.chaudhury50@gmail.com last updated…
Question Number 42106 by rahul 19 last updated on 18/Aug/18 Answered by tanmay.chaudhury50@gmail.com last updated on 18/Aug/18 $$\mathrm{5}{c}_{\mathrm{2}} ×\mathrm{2}!+\mathrm{5}{c}_{\mathrm{3}} ×\mathrm{3}!+\mathrm{5}{c}_{\mathrm{4}} ×\mathrm{4}!+\mathrm{5}{c}_{\mathrm{5}} ×\mathrm{5}! \\ $$$$=\mathrm{5}{p}_{\mathrm{2}} +\mathrm{5}{p}_{\mathrm{3}}…
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Question Number 107451 by mr W last updated on 11/Aug/20 $${How}\:{many}\:{words}\:{can}\:{you}\:{form}\:{using} \\ $$$${the}\:{letters}\:\:{in}\:\boldsymbol{{UNUSUALLY}} \\ $$$${such}\:{that}\:{no}\:{same}\:{letters}\:{are}\:\:{next} \\ $$$${to}\:{each}\:{other}? \\ $$$$ \\ $$$$\left[{Answer}:\:\mathrm{10200}\right] \\ $$ Commented by…
Question Number 41824 by Tawa1 last updated on 13/Aug/18 $$\mathrm{if}\:\:\:\overset{\mathrm{n}} {\:}\mathrm{C}_{\mathrm{5}} \:=\:\overset{\mathrm{n}} {\:}\mathrm{C}_{\mathrm{11}} \:\:\:\mathrm{find}\:\:\:\:\:\:\overset{\mathrm{18}} {\:}\mathrm{C}_{\mathrm{n}} \\ $$ Answered by $@ty@m last updated on 13/Aug/18 $$\:\:^{{n}}…
Question Number 107327 by pticantor last updated on 10/Aug/20 $$\mathrm{1}\leqslant{p}\leqslant{k}\leqslant{n} \\ $$$${show}\:{that}\:\underset{{k}={p}} {\overset{{n}} {\sum}}\boldsymbol{{C}}_{{k}−\mathrm{1}} ^{{p}−\mathrm{1}} =\boldsymbol{{C}}_{{n}} ^{{p}} \\ $$$${please}\:{i}\:{need}\:{help} \\ $$ Terms of Service Privacy…
Question Number 172817 by Mikenice last updated on 01/Jul/22 Answered by som(math1967) last updated on 02/Jul/22 $$\sqrt{\mathrm{2}+\sqrt{\mathrm{2}+\sqrt{\mathrm{2}\left(\mathrm{1}+{cos}\mathrm{8}\theta\right)}}} \\ $$$$\sqrt{\mathrm{2}+\sqrt{\mathrm{2}+\mathrm{2}{cos}\mathrm{4}\theta}} \\ $$$$\sqrt{\mathrm{2}+\sqrt{\mathrm{2}\left(\mathrm{1}+{cos}\mathrm{4}\theta\right)}} \\ $$$$\sqrt{\mathrm{2}+\mathrm{2}{cos}\mathrm{2}\theta}=\sqrt{\mathrm{2}\left(\mathrm{1}+{cos}\mathrm{2}\theta\right)}=\mathrm{2}{cos}\theta \\ $$…