Question Number 220743 by Spillover last updated on 18/May/25 Answered by som(math1967) last updated on 18/May/25 $$\:{No}\:{of}\:{way}\:\mathrm{4}\:{soldiers}\:{can}\:{be}\:{chosen} \\ $$$$=\:^{\mathrm{9}} {C}_{\mathrm{4}} =\mathrm{126} \\ $$$${when}\:{particular}\:{soldier}\:{included} \\ $$$$=\:^{\mathrm{8}}…
Question Number 220739 by Spillover last updated on 18/May/25 Answered by mr W last updated on 18/May/25 $$\left.\mathrm{1}\right) \\ $$$$\frac{\mathrm{7}!}{\mathrm{2}!\mathrm{2}!}=\mathrm{1260} \\ $$$$\left.\mathrm{2}\right) \\ $$$$\mathrm{1260}−\mathrm{2}×\frac{\mathrm{6}!}{\mathrm{2}!\mathrm{2}!}=\mathrm{1260}−\mathrm{360}=\mathrm{900} \\…
Question Number 219936 by Razafitiana last updated on 04/May/25 $$\mathrm{Prove}\:\mathrm{that}:\forall\mathrm{n}\in\mathrm{IN} \\ $$$$\underset{\:\mathrm{n}} {\int}^{\:\mathrm{n}+\mathrm{1}} \mathrm{ln}\left(\mathrm{t}\right)\mathrm{dt}\leqslant\mathrm{ln}\left(\mathrm{n}+\frac{\mathrm{1}}{\mathrm{2}}\right) \\ $$ Answered by MrGaster last updated on 04/May/25 $$\underset{\:\mathrm{n}} {\int}^{\:\mathrm{n}+\mathrm{1}}…
Question Number 219527 by mr W last updated on 27/Apr/25 Commented by Nicholas666 last updated on 27/Apr/25 $$\frac{\mathrm{1}}{\mathrm{48019}} \\ $$$$ \\ $$ Commented by mr…
Question Number 218578 by mr W last updated on 13/Apr/25 $$\mathrm{10}\:{couples}\:{are}\:{invited}\:{to}\:{a}\:{dinner}. \\ $$$${after}\:{the}\:{dinner}\:{they}\:{form}\:{pairs}\: \\ $$$${to}\:{dance}.\:{in}\:{how}\:{many}\:{ways}\:{can}\:{they} \\ $$$${do}\:{this}, \\ $$$$\left.\mathrm{1}\right)\:{generally} \\ $$$$\left.\mathrm{2}\right)\:{a}\:{man}\:{should}\:{dance}\:{with}\:{a}\:{woman} \\ $$$$\left.\mathrm{3}\left.\right)\:{as}\:\mathrm{2}\right),\:{but}\:{two}\:{special}\:{couples} \\ $$$$\:\:\:\:\:{should}\:{not}\:{dance}\:{with}\:{each}\:{other}…
Question Number 218445 by mr W last updated on 10/Apr/25 $${there}\:{are}\:\mathrm{100}\:{students}\:{in}\:{a}\:{school}. \\ $$$${it}\:{is}\:{found}\:{out}\:{that}\:{each}\:{student}\: \\ $$$${should}\:{select}\:{at}\:{least}\:\mathrm{4}\:{courses},\:{so}\: \\ $$$${that}\:{no}\:{two}\:{students}\:{have}\:{the}\:{same}\: \\ $$$${selection}.\: \\ $$$${how}\:{many}\:{different}\:{courses}\:{does}\: \\ $$$${the}\:{school}\:{offer}? \\ $$…
Question Number 218310 by mr W last updated on 06/Apr/25 $$\mathrm{10}\:{couples}\:{are}\:{invited}\:{to}\:{a}\:{dinner} \\ $$$${and}\:{should}\:{be}\:{seated}\:{at}\:{a}\:{round}\:{table}. \\ $$$${in}\:{how}\:{many}\:{ways}\:{can}\:{the}\:{host}\:{do} \\ $$$${this}, \\ $$$$\left.\mathrm{1}\right)\:{generally}. \\ $$$$\left.\mathrm{2}\right)\:{if}\:{the}\:{husband}\:{and}\:{the}\:{wife}\:{of} \\ $$$$\:\:\:\:\:{each}\:{couple}\:{should}\:{sit}\:{together}. \\ $$$$\left.\mathrm{3}\right)\:{if}\:{no}\:{two}\:{men}\:{should}\:{sit}\:{next}…
Question Number 218299 by mr W last updated on 05/Apr/25 $$\mathrm{10}\:{couples}\:{are}\:{invited}\:{to}\:{a}\:{dinner}\:{and} \\ $$$${should}\:{be}\:{seated}\:{at}\:{a}\:{round}\:{table}. \\ $$$${in}\:{how}\:{many}\:{ways}\:{can}\:{the}\:{host}\:{do} \\ $$$${this}, \\ $$$$\left.\mathrm{1}\right)\:{generally} \\ $$$$\left.\mathrm{2}\right)\:{if}\:{two}\:{men}\:{should}\:{not}\:{sit}\:{next} \\ $$$$\:\:\:\:\:{to}\:{each}\:{other} \\ $$$$\left.\mathrm{3}\left.\right)\:{as}\:\mathrm{2}\right),\:{but}\:{two}\:{speicial}\:{couples}\:…
Question Number 218169 by vile last updated on 31/Mar/25 $${P}\left(\mathrm{5},\mathrm{6}\right)=\frac{\mathrm{15}!}{\left(\mathrm{15}−\mathrm{6}\right)}\:=\:\frac{\mathrm{15}!}{\mathrm{9}!}\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:=\frac{\mathrm{15}×\mathrm{14}×\mathrm{131}×\mathrm{2}×\mathrm{11}×\mathrm{10}×\mathrm{9}×\mathrm{8}×\mathrm{7}×\mathrm{6}×\mathrm{5}×\mathrm{4}×\mathrm{3}×\mathrm{2}×\mathrm{1}}{\mathrm{9}×\mathrm{8}×\mathrm{7}×\mathrm{6}×\mathrm{5}×\mathrm{4}×\mathrm{3}×\mathrm{2}×} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:=\mathrm{15}×\mathrm{14}×\mathrm{13}×\mathrm{12}×\mathrm{11}×\mathrm{10} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:=\mathrm{3},\mathrm{603},\mathrm{600} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\: \\ $$ Terms of Service Privacy Policy…
Question Number 218129 by mr W last updated on 30/Mar/25 $${how}\:{many}\:{different}\:{words}\:{can}\:{be} \\ $$$${formed}\:{from}\:{the}\:{word}\: \\ $$$$\boldsymbol{\mathrm{MATHEMATICS}}? \\ $$$${note}:\:\:{here}\:{a}\:{word}\:{should}\:{have}\:{at}\: \\ $$$${least}\:{two}\:{letters},\:{but}\:{mustn}'{t}\:{have}\:{a} \\ $$$${meaning}. \\ $$ Answered by…