Question Number 50258 by rahul 19 last updated on 15/Dec/18 $${A}\:{delegation}\:{of}\:\mathrm{4}\:{students}\:{is}\:{to}\:{be} \\ $$$${selected}\:{from}\:{a}\:{total}\:{of}\:\mathrm{12}\:{students}. \\ $$$${In}\:{how}\:{many}\:{ways}\:{can}\:{the}\:{delegation} \\ $$$${be}\:{selected}\:{if}: \\ $$$$\left.\mathrm{1}\right)\:\mathrm{2}\:{particular}\:{students}\:{wish}\:{to}\:{be}\: \\ $$$${included}\:{together}\:{only}\:{in}\:{the}\:{delegation}? \\ $$$$\left.\mathrm{2}\right)\:\mathrm{2}\:{particular}\:{students}\:{refuse}\:{to}\:{be}\: \\ $$$${together}\:{and}\:\mathrm{2}\:{other}\:{particular}\:{students}…
Question Number 115769 by bemath last updated on 28/Sep/20 $${There}\:{are}\:\mathrm{3}\:{teachers}\:{and}\:\mathrm{6}\:{students} \\ $$$${who}\:{will}\:{sit}\:{on}\:{the}\:\mathrm{9}\:{available}\:{seats}.\:{many} \\ $$$${arrangements}\:{they}\:{sit}\:{if}\:{each}\: \\ $$$${teacher}\:{is}\:{flanked}\:{by}\:\mathrm{2}\:{students} \\ $$ Answered by mr W last updated on…
Question Number 181251 by cortano1 last updated on 23/Nov/22 Commented by cortano1 last updated on 23/Nov/22 $$\:\mathrm{A}\:\mathrm{photograph}\:\mathrm{is}\:\mathrm{to}\:\mathrm{be}\:\mathrm{taken}\:\mathrm{of}\:\mathrm{seven}\:\mathrm{girls}\: \\ $$$$\:\mathrm{standing}\:\mathrm{in}\:\mathrm{two}\:\mathrm{rows},\:\mathrm{with}\:\mathrm{one}\:\mathrm{row} \\ $$$$\mathrm{in}\:\mathrm{front}\:\mathrm{of}\:\mathrm{the}\:\mathrm{other}.\:\mathrm{The}\:\mathrm{tallest}\:\mathrm{girl}\: \\ $$$$\mathrm{must}\:\mathrm{be}\:\mathrm{in}\:\mathrm{the}\:\mathrm{midlle}\:\mathrm{of}\:\mathrm{the}\:\mathrm{row}\:\mathrm{of} \\ $$$$\mathrm{three}\:\mathrm{and}\:\mathrm{the}\:\mathrm{shortest}\:\mathrm{girl}\:\mathrm{must}\:\mathrm{be}…
Question Number 50008 by rahul 19 last updated on 13/Dec/18 $$\mathrm{5}−{digit}\:{number}\:{divisible}\:{by}\:\mathrm{3}\:{formed} \\ $$$${using}\:\mathrm{0},\mathrm{1},\mathrm{2},\mathrm{3},\mathrm{4},\mathrm{5}\:{without}\:{repetition}. \\ $$$${Total}\:{number}\:{of}\:{such}\:{no}.{s}\:{is}\:? \\ $$ Commented by rahul 19 last updated on 13/Dec/18…
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…