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…
Question Number 54860 by Tinkutara last updated on 13/Feb/19 Commented by Tinkutara last updated on 14/Feb/19 $${But}\:{answer}\:{is} \\ $$$$\frac{\mathrm{1}}{\mathrm{2}}\left(\mathrm{2}{n}−{k}^{\mathrm{2}} +{k}−\mathrm{2}\right) \\ $$ Answered by kaivan.ahmadi…
Question Number 54740 by gunawan last updated on 10/Feb/19 $${Prove}\:{that} \\ $$$$\mathrm{1}.\begin{pmatrix}{{n}}\\{{r}}\end{pmatrix}\:=\:\begin{pmatrix}{{n}−\mathrm{1}}\\{\:\:\:\:{r}}\end{pmatrix}\:+\:\begin{pmatrix}{{n}−\mathrm{1}}\\{\:{r}−\mathrm{1}}\end{pmatrix} \\ $$$$\mathrm{2}.\begin{pmatrix}{{n}}\\{{r}}\end{pmatrix}\:+\begin{pmatrix}{\:\:\:{n}}\\{{r}−\mathrm{1}}\end{pmatrix}\:=\:\begin{pmatrix}{{n}+\mathrm{1}}\\{\:\:\:\:{r}}\end{pmatrix}\: \\ $$$$\mathrm{3}.\:\begin{pmatrix}{{n}}\\{\mathrm{0}}\end{pmatrix}+\begin{pmatrix}{{n}}\\{\mathrm{1}}\end{pmatrix}+\begin{pmatrix}{{n}}\\{\mathrm{2}}\end{pmatrix}+..+\begin{pmatrix}{{n}}\\{{n}}\end{pmatrix}=\mathrm{2}^{{n}} \\ $$ Answered by Kunal12588 last updated on 10/Feb/19…
Question Number 54698 by mr W last updated on 09/Feb/19 $${How}\:{many}\:{words}\:{with}\:{at}\:{least}\:\mathrm{2}\:{letters} \\ $$$${can}\:{be}\:{formed}\:{using}\:{the}\:{letters}\:{from} \\ $$$${TINKUTARA}? \\ $$ Answered by afachri last updated on 09/Feb/19 Commented…