Question Number 49982 by pieroo last updated on 12/Dec/18 $$\mathrm{If}\:\frac{\mathrm{n}_{\mathrm{P}_{\mathrm{r}} } }{\mathrm{n}_{\mathrm{C}_{\mathrm{r}} } }\:−\mathrm{1}=\mathrm{5},\:\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{r} \\ $$ Answered by ajfour last updated on 13/Dec/18 $$\:^{{n}} {P}_{{r}}…
Question Number 115408 by mr W last updated on 25/Sep/20 $${how}\:{many}\:\mathrm{6}\:{digit}\:{numbers}\:{exist} \\ $$$${which}\:{are}\:{divisible}\:{by}\:\mathrm{11}\:{and}\:{have}\:{no} \\ $$$${repeating}\:{digits}? \\ $$ Answered by Olaf last updated on 26/Sep/20 $$\mathrm{N}\:=\:{a}_{\mathrm{5}}…
Question Number 115387 by bemath last updated on 25/Sep/20 Commented by bemath last updated on 25/Sep/20 $${p}=\:\frac{\:^{\mathrm{8}} {C}_{\mathrm{4}} ×!\mathrm{4}}{\mathrm{8}!}\:=\:\frac{\frac{\mathrm{8}!}{\mathrm{4}!.\mathrm{4}!}\:×\:\mathrm{9}}{\mathrm{8}!}\:=\:\frac{\mathrm{9}}{\mathrm{576}} \\ $$$$ \\ $$ Commented by…
Question Number 180899 by alcohol last updated on 19/Nov/22 $${H}_{{n}} \:=\:\underset{{k}=\mathrm{1}} {\overset{{n}} {\sum}}\frac{\mathrm{1}}{{k}} \\ $$$${show}\:{that}\:{H}_{\mathrm{2}{n}} \:−\:{H}_{{n}} \:=\:\underset{{k}=\mathrm{1}} {\overset{{n}} {\sum}}\left(\frac{\mathrm{1}}{\mathrm{2}{k}−\mathrm{1}}−\frac{\mathrm{1}}{\mathrm{2}{k}}\right) \\ $$ Answered by Frix last…
Question Number 180890 by Tawa11 last updated on 18/Nov/22 We have 7 sets with 2 subsets each (yes and no are the 2 subsets of…
Question Number 180773 by Acem last updated on 17/Nov/22 $${How}\:{many}\:{triangles}\:{can}\:{be}\:{formed}\:{from} \\ $$$$\:{non}−{adjacent}\:{vertices}\:{of}\:{a}\:{regular}\:{polygon} \\ $$$$\:{that}\:{it}\:{angle}\:{is}\:\mathrm{177}^{\:°} \:? \\ $$ Answered by mr W last updated on 17/Nov/22…
Question Number 115230 by bemath last updated on 24/Sep/20 $$\mathrm{2}\:{women}\:{and}\:\mathrm{4}\:{men}\:{will}\:{sit}\:{on}\:{the} \\ $$$$\mathrm{8}\:{available}\:{seats}\:{and}\:{surround}\: \\ $$$${the}\:{round}\:{table}\:.\:{The}\:{many}\:{possible} \\ $$$${arrangements}\:{of}\:{them}\:{sitting} \\ $$$${if}\:{they}\:{sat}\:{randomly} \\ $$ Commented by mr W last…
Question Number 115170 by bobhans last updated on 24/Sep/20 $$\left(\mathrm{1}\right){Given}\:\frac{{P}\:_{{n}−\mathrm{1}} ^{\mathrm{2}{n}+\mathrm{1}} }{{P}\:_{{n}} ^{\mathrm{2}{n}−\mathrm{1}} }\:=\:\frac{\mathrm{3}}{\mathrm{5}}\:,\:{find}\:{n}\:=\:? \\ $$$$\left(\mathrm{2}\right)\:{in}\:{how}\:{many}\:{ways}\:{can}\:\mathrm{6}\:{persons} \\ $$$${stand}\:{in}\:{a}\:{queue}? \\ $$$$\left(\mathrm{3}\right)\:{how}\:{many}\:{different}\:\mathrm{4}\:{letter}\:{words} \\ $$$${can}\:{be}\:{formed}\:{by}\:{using}\:{letters}\:{of}\: \\ $$$${EDUCATION}\:{using}\:{each}\:{letter}\:{at}\: \\…
Question Number 180585 by mr W last updated on 14/Nov/22 $${there}\:{are}\:\mathrm{5}\:{points}\:{on}\:{a}\:{line}\:{and}\:\mathrm{4}\: \\ $$$${points}\:{on}\:{a}\:{parallel}\:{line}. \\ $$$${how}\:{many}\:{quadrilaterals}\:{can}\:{be}\: \\ $$$${formed}\:{with}\:{these}\:{points}\:{as}\: \\ $$$${vertrices}? \\ $$ Answered by nikif99 last…
Question Number 49482 by rahul 19 last updated on 07/Dec/18 $${Find}\:{number}\:{of}\:\mathrm{4}−{letter}\:{words}\:{which} \\ $$$${can}\:{be}\:{formed}\:{using}\:{the}\:{letters}\:{of}\: \\ $$$${the}\:{word}\:'{ALLAHABAD}'\:{such}\:{that}: \\ $$$${NO}\:{repetition}\:{of}\:{letter}\:{and}\:{word}\:{should} \\ $$$${start}\:“{either}''\:{from}\:{H}\:“{or}''\:{ends}\:{with}\:{D}\:? \\ $$ Commented by tanmay.chaudhury50@gmail.com last…