Question Number 57688 by Tawa1 last updated on 10/Apr/19 $$\:\:\mathrm{Solve}\:\mathrm{for}\:\:\mathrm{n}:\:\:\:\:\:\:\:\:\underset{\mathrm{i}} {\overset{\mathrm{n}\:−\:\mathrm{1}} {\sum}}\:\:\:\overset{\mathrm{n}} {\:}\mathrm{C}_{\mathrm{i}} \:\mathrm{2}^{\mathrm{i}} \:\:=\:\:\mathrm{65},\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{n}\:\in\:\mathbb{Z}^{+} .\:\:\:\:\mathrm{where}\:\:\mathrm{zero}\:\mathrm{is}\: \\ $$$$\:\:\mathrm{included} \\ $$ Commented by tanmay.chaudhury50@gmail.com last updated…
Question Number 188551 by mr W last updated on 03/Mar/23 $${you}\:{randomly}\:{select}\:{a}\:\mathrm{5}\:{digit}\:{number}. \\ $$$${what}'{s}\:{the}\:{probability}\:{that}\:{this}\:{number} \\ $$$${has}\:{exactly}\:\mathrm{3}\:{different}\:{digits}? \\ $$ Answered by mr W last updated on 03/Mar/23…
Question Number 57363 by Tawa1 last updated on 03/Apr/19 Commented by Tawa1 last updated on 03/Apr/19 $$\mathrm{Please}\:\mathrm{help}.\:\mathrm{my}\:\mathrm{problem}\:\mathrm{is}\:\mathrm{from}\:\:\frac{\mathrm{2}^{\mathrm{m}} \:.\:\mathrm{m}\left(\mathrm{m}\:+\:\mathrm{1}\right)\left(\mathrm{m}\:+\:\mathrm{2}\right)\:….\:\left(\mathrm{2m}\:−\:\mathrm{1}\right)}{\mathrm{1}.\mathrm{3}.\mathrm{5}.\:…….\:\left(\mathrm{2m}\:−\:\mathrm{1}\right)} \\ $$$$\mathrm{now}\:\mathrm{why}\:\mathrm{did}\:\mathrm{they}\:\mathrm{multiply}\:\mathrm{Numerator}\:\mathrm{and}\:\mathrm{denominator}\:\mathrm{by} \\ $$$$\left(\mathrm{m}\:−\:\mathrm{1}\right)!.\:\mathrm{2m}\:\:\mathrm{to}\:\mathrm{get}\:… \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\frac{\mathrm{2}^{\mathrm{m}} \:.\:\mathrm{m}\left(\mathrm{m}\:+\:\mathrm{1}\right)\left(\mathrm{m}\:+\:\mathrm{2}\right)\:….\:\left(\mathrm{2m}\:−\:\mathrm{1}\right)\:×\:\left(\mathrm{m}\:−\:\mathrm{1}\right)!.\:\mathrm{2m}}{\left[\mathrm{1}.\mathrm{3}.\mathrm{5}.\:…….\:\left(\mathrm{2m}\:−\:\mathrm{1}\right)\right]\:…….\:.\:\left(\mathrm{m}\:−\:\mathrm{1}\right)!\:.\:\mathrm{2m}\:}…
Question Number 57336 by Tawa1 last updated on 02/Apr/19 $$\mathrm{If}\:\:\mathrm{n}\:\mathrm{be}\:\mathrm{even},\:\mathrm{show}\:\mathrm{that}\:\mathrm{the}\:\mathrm{expression}\:\:\:\:\frac{\mathrm{n}\left(\mathrm{n}\:+\:\mathrm{2}\right)\left(\mathrm{n}\:+\:\mathrm{4}\right)\:…\:\left(\mathrm{2n}\:−\:\mathrm{2}\right)}{\mathrm{1}.\mathrm{3}.\mathrm{5}\:…\:\left(\mathrm{n}\:−\:\mathrm{1}\right)} \\ $$$$\mathrm{simplify}\:\mathrm{to}\:\:\mathrm{2}^{\mathrm{n}\:−\:\mathrm{1}} \\ $$ Answered by Smail last updated on 03/Apr/19 $${A}=\frac{{n}\left({n}+\mathrm{2}\right)\left({n}+\mathrm{4}\right)…\left(\mathrm{2}{n}−\mathrm{2}\right)}{\mathrm{1}.\mathrm{3}.\mathrm{5}…\left({n}−\mathrm{1}\right)} \\ $$$${n}=\mathrm{2}{m} \\…
Question Number 188362 by mr W last updated on 28/Feb/23 $${find}\:{the}\:{number}\:{of}\:\mathrm{5}\:{digit}\:{natural} \\ $$$${numbers}\:{with}\:{strictly}\:{ascending}\: \\ $$$${digits}\:{whose}\:{sum}\:{is}\:\mathrm{20}. \\ $$$${example}:\:\mathrm{12458}\:{is}\:{such}\:{a}\:{number} \\ $$ Answered by ARUNG_Brandon_MBU last updated on…
Question Number 188301 by mr W last updated on 28/Feb/23 $${Find}\:{the}\:{number}\:{of}\:{triangles}\:{with} \\ $$$${integer}\:{side}\:{lengths}\:{and}\:{perimeter}\:{p}. \\ $$ Commented by mr W last updated on 28/Feb/23 $${as}\:{Q}\mathrm{188239},\:{but}\:{in}\:{general}\:{case}. \\…
Question Number 57046 by mr W last updated on 29/Mar/19 Commented by mr W last updated on 29/Mar/19 $${reposted} \\ $$$${Question}\:{from}\:{Tinkutara}\:{sir} \\ $$ Terms of…
Question Number 57048 by mr W last updated on 29/Mar/19 Commented by mr W last updated on 29/Mar/19 $${reposted} \\ $$$${Question}\:{from}\:{Tinkutara}\:{sir} \\ $$ Answered by…
Question Number 57042 by mr W last updated on 29/Mar/19 Commented by mr W last updated on 29/Mar/19 $${reposted} \\ $$$${Question}\:{from}\:{Tinkutara}\:{sir} \\ $$$$ \\ $$$${i}\:{found}\:{these}\:{unsolved}\:{questions}\:{in}…
Question Number 56961 by pete last updated on 27/Mar/19 $$\mathrm{Out}\:\mathrm{of}\:\mathrm{6}\:\mathrm{mathematicians}\:\mathrm{and}\:\mathrm{7}\:\mathrm{physicists} \\ $$$$\mathrm{a}\:\mathrm{committee}\:\mathrm{consisting}\:\mathrm{of}\:\mathrm{3}\:\mathrm{mathematicians} \\ $$$$\mathrm{and}\:\mathrm{3}\:\mathrm{physicists}\:\mathrm{is}\:\mathrm{to}\:\mathrm{be}\:\mathrm{formed}.\:\mathrm{In}\:\mathrm{how} \\ $$$$\mathrm{many}\:\mathrm{ways}\:\mathrm{can}\:\mathrm{this}\:\mathrm{be}\:\mathrm{done}\:\mathrm{if}\:\mathrm{two}\: \\ $$$$\mathrm{particular}\:\mathrm{mathematicians}\:\mathrm{cannot}\:\mathrm{be} \\ $$$$\mathrm{on}\:\mathrm{the}\:\mathrm{commitee}? \\ $$ Answered by tanmay.chaudhury50@gmail.com…