Question Number 56025 by pieroo last updated on 08/Mar/19 $$\mathrm{Find}\:\mathrm{the}\:\mathrm{probability}\:\mathrm{that}\:\mathrm{a}\:\mathrm{student} \\ $$$$\mathrm{arranging}\:\mathrm{the}\:\mathrm{letters}\:\mathrm{of}\:\mathrm{the}\:\mathrm{word} \\ $$$$\mathrm{MATHEMATICS}\:\mathrm{will}\:\mathrm{make}\:\mathrm{all}\:\mathrm{the} \\ $$$$\mathrm{vowels}\:\mathrm{be}\:\mathrm{together}\:\mathrm{in}\:\mathrm{any}\:\mathrm{arrangement} \\ $$$$\mathrm{he}\:\mathrm{or}\:\mathrm{she}\:\mathrm{does}. \\ $$ Answered by tanmay.chaudhury50@gmail.com last updated…
Question Number 55502 by mr W last updated on 25/Feb/19 Commented by mr W last updated on 25/Feb/19 $${as}\:{Q}\mathrm{55468},\:{but}\:{passwords}\:{with}\:\mathrm{6} \\ $$$${characters}. \\ $$ Answered by…
Question Number 55468 by peter frank last updated on 24/Feb/19 Answered by mr W last updated on 25/Feb/19 $${to}\:{choose}\:\mathrm{4}\:{characters}\:{there}\:{are}\:{three} \\ $$$${cases}: \\ $$$${case}\:\mathrm{1}:\:{two}\:{letters},\:{one}\:{digit},\:{one}\:{symbol} \\ $$$${to}\:{choose}\:\mathrm{2}\:{letters}\:{there}\:{are}\:{C}_{\mathrm{2}}…
Question Number 120954 by cantor last updated on 04/Nov/20 $$\boldsymbol{{shown}}\:\boldsymbol{{that}} \\ $$$$ \\ $$$$\:\:\:\boldsymbol{{n}}!=\underset{\boldsymbol{{k}}=\mathrm{0}} {\overset{\boldsymbol{{n}}} {\sum}}\left(−\mathrm{1}\right)^{\boldsymbol{{k}}} \left(_{\:\boldsymbol{{k}}} ^{\:\boldsymbol{{n}}} \right)\left(\boldsymbol{{n}}−\boldsymbol{{k}}\right)^{\boldsymbol{{n}}} \\ $$$$\boldsymbol{{please}}\:\boldsymbol{{help}}\:\boldsymbol{{me}} \\ $$ Terms of…
Question Number 55192 by Learner last updated on 19/Feb/19 $${what}\:{will}\:{be}\:{the}\:{numbers}\:{of}\:{zeroes}\:{in}\:{the}\:{expension}\:{of} \\ $$$$\left.{a}\right)\:\mathrm{100}!×\mathrm{25}! \\ $$$$\left.{b}\right)\:\mathrm{100}!+\mathrm{25}! \\ $$$$ \\ $$$${please}\:{help} \\ $$ Commented by MJS last updated…
Question Number 55119 by pieroo last updated on 17/Feb/19 $$\mathrm{How}\:\mathrm{many}\:\mathrm{numbers},\:\mathrm{divisible}\:\mathrm{by}\:\mathrm{5},\:\mathrm{can} \\ $$$$\mathrm{be}\:\mathrm{made}\:\mathrm{with}\:\mathrm{the}\:\mathrm{digits}\:\mathrm{2},\mathrm{3},\mathrm{4}\:\mathrm{and}\:\mathrm{5}\:\mathrm{where} \\ $$$$\mathrm{no}\:\mathrm{digit}\:\mathrm{is}\:\mathrm{being}\:\mathrm{used}\:\mathrm{more}\:\mathrm{than}\:\mathrm{once} \\ $$$$\mathrm{in}\:\mathrm{each}\:\mathrm{number}? \\ $$ Commented by Tawa1 last updated on 17/Feb/19…
Question Number 55115 by aseerimad last updated on 17/Feb/19 Commented by aseerimad last updated on 17/Feb/19 please help.... Commented by mr W last updated on 17/Feb/19…
Question Number 55099 by Joel578 last updated on 17/Feb/19 $$\mathrm{Show}\:\mathrm{that}\:\mathrm{for}\:{n}\:\in\:\mathbb{N}, \\ $$$$\underset{{r}=\mathrm{0}} {\overset{{n}} {\sum}}\:{P}_{{r}} ^{{n}} \:=\:\lfloor{n}!\:{e}\rfloor \\ $$$$\mathrm{where}\:\lfloor{x}\rfloor\:\mathrm{denotes}\:\mathrm{the}\:\mathrm{greatest}\:\mathrm{integer}\:\leqslant\:{x} \\ $$$$\mathrm{and}\:{P}_{{r}} ^{{n}} \:=\:\frac{{n}!}{\left({n}\:−\:{r}\right)!} \\ $$ Answered…
Question Number 55100 by aseerimad last updated on 17/Feb/19 Commented by aseerimad last updated on 17/Feb/19 how no.14 is done?.....pls help Commented by aseerimad last updated on 17/Feb/19 thank you sir. But can u please convert the answer to the form that I gave?…
Question Number 120431 by john santu last updated on 31/Oct/20 Commented by john santu last updated on 31/Oct/20 $${old}\:{unswered}\:{question} \\ $$ Commented by mr W…