Question Number 155075 by mr W last updated on 24/Sep/21 Commented by mr W last updated on 24/Sep/21 $${with}\:{exactly}\:{n}\:{turns}.\:\left(\mathrm{1}\leqslant{n}\leqslant\mathrm{15}\right) \\ $$$${the}\:{example}\:{above}\:{shows}\:{a}\:{route} \\ $$$${with}\:\mathrm{7}\:{turns}. \\ $$…
Question Number 88876 by Joel578 last updated on 13/Apr/20 $$\mathrm{Given}\:\mathrm{a}\:\mathrm{10}−\mathrm{digit}\:\mathrm{number}\:{X}\:=\:\mathrm{1345789026} \\ $$$$\mathrm{How}\:\mathrm{many}\:\mathrm{10}−\mathrm{digit}\:\mathrm{number}\:\mathrm{that}\:\mathrm{can}\:\mathrm{be}\:\mathrm{made} \\ $$$$\mathrm{using}\:\mathrm{every}\:\mathrm{digit}\:\mathrm{from}\:{X},\:\mathrm{with}\:\mathrm{condition}: \\ $$$$\mathrm{If}\:\mathrm{a}\:\mathrm{number}\:{n}\:\:\mathrm{is}\:\mathrm{located}\:\mathrm{in}\:{k}^{{th}} \:\mathrm{position}\:\mathrm{of}\:{X},\:\mathrm{then} \\ $$$$\mathrm{the}\:\mathrm{new}\:\mathrm{created}\:\mathrm{number}\:\mathrm{must}\:\mathrm{not}\:\mathrm{contain} \\ $$$$\mathrm{number}\:{n}\:\mathrm{in}\:{k}^{{th}} \:\mathrm{position} \\ $$$$ \\…
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Question Number 154268 by liberty last updated on 16/Sep/21 Commented by mr W last updated on 16/Sep/21 $$\mathrm{8}!=\mathrm{40320} \\ $$ Commented by liberty last updated…
Question Number 22820 by Physics lover last updated on 22/Oct/17 $${total}\:{number}\:{of}\:{permutations}\:{of} \\ $$$${five}\:{abjects}\:\rightarrow\:{A},{A},{A},{B},{B}\: \\ $$$${in}\:{a}\:{circle}? \\ $$ Commented by ajfour last updated on 22/Oct/17 $${four}\:.…
Question Number 153714 by pete last updated on 09/Sep/21 $$\mathrm{How}\:\mathrm{many}\:\mathrm{three}−\mathrm{digit}\:\mathrm{numbers}\:\mathrm{can}\:\mathrm{be} \\ $$$$\mathrm{formed}\:\mathrm{using}\:\mathrm{the}\:\mathrm{digits}\:\mathrm{2},\mathrm{3},\mathrm{5},\mathrm{7},\mathrm{8}\:\mathrm{if}\: \\ $$$$\mathrm{the}\:\mathrm{number}\:\mathrm{is}\:\mathrm{odd}\:\mathrm{and}\:\mathrm{no}\:\mathrm{digit}\:\mathrm{is}\:\mathrm{repeted}? \\ $$ Answered by EDWIN88 last updated on 09/Sep/21 $$=\:{P}_{\mathrm{1}} ^{\:\mathrm{3}}…
Question Number 87975 by ajfour last updated on 07/Apr/20 Commented by ajfour last updated on 07/Apr/20 $${Find}\:{radius}\:{of}\:{circle}. \\ $$ Commented by Tony Lin last updated…
Question Number 22435 by Tinkutara last updated on 18/Oct/17 $${C}_{\mathrm{0}} \:^{\mathrm{2}{n}} {C}_{{n}} −{C}_{\mathrm{1}} \:^{\mathrm{2}{n}−\mathrm{2}} {C}_{{n}} +{C}_{\mathrm{2}} \:^{\mathrm{2}{n}−\mathrm{4}} {C}_{{n}} \:…. \\ $$$$\mathrm{equals}\:\mathrm{to} \\ $$ Terms of…
Question Number 87933 by john santu last updated on 07/Apr/20 $$\mathrm{how}\:\mathrm{many}\:\mathrm{terms}\:\mathrm{are}\:\mathrm{there} \\ $$$$\mathrm{in}\:\left(\mathrm{x}^{\mathrm{2}} +\mathrm{x}+\mathrm{1}\right)^{\mathrm{11}} \:? \\ $$ Commented by mr W last updated on 07/Apr/20…
Question Number 87790 by mathocean1 last updated on 06/Apr/20 $$\mathrm{How}\:\mathrm{many}\:\mathrm{handshakes}\:\mathrm{are}\:\mathrm{exchanged} \\ $$$$\mathrm{betwen}\:\mathrm{27}\:\mathrm{boys}? \\ $$ Answered by TANMAY PANACEA. last updated on 06/Apr/20 $$\mathrm{27}{C}_{\mathrm{2}} \\ $$$$=\frac{\mathrm{27}!}{\mathrm{2}!\mathrm{25}!}=\frac{\mathrm{27}×\mathrm{26}}{\mathrm{2}}=\mathrm{351}…