Question Number 220744 by Spillover last updated on 18/May/25 Answered by mr W last updated on 18/May/25 $${each}\:{match}\:{has}\:{three}\:{possible} \\ $$$${results} \\ $$$$\mathrm{12}\:{matches}\:{have}\:\mathrm{3}^{\mathrm{12}} =\mathrm{531}\:\mathrm{441} \\ $$$$\:{possible}\:{results}…
Question Number 220741 by Spillover last updated on 18/May/25 Answered by som(math1967) last updated on 18/May/25 $$\:\:^{\mathrm{9}} {P}_{\mathrm{4}} =\mathrm{3024} \\ $$ Commented by Spillover last…
Question Number 220740 by Spillover last updated on 18/May/25 Answered by mr W last updated on 18/May/25 $$\mathrm{52}\:{cards}:\:\mathrm{26}\:{red}\:{and}\:\mathrm{26}\:{black} \\ $$$${to}\:{select}\:\mathrm{13}\:{cards}\:{there}\:{are}\:{totally} \\ $$$${C}_{\mathrm{13}} ^{\mathrm{52}} \:{possibilities} \\…
Question Number 220743 by Spillover last updated on 18/May/25 Answered by som(math1967) last updated on 18/May/25 $$\:{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}…