Question Number 130634 by EDWIN88 last updated on 27/Jan/21 Answered by liberty last updated on 27/Jan/21 $$\mathrm{coefficient}\:\mathrm{of}\:\mathrm{x}^{\mathrm{8}} \:\mathrm{from}\:\left(\mathrm{1}+\frac{\mathrm{x}^{\mathrm{2}} }{\mathrm{2}!}+\frac{\mathrm{x}^{\mathrm{4}} }{\mathrm{4}!}+\frac{\mathrm{x}^{\mathrm{6}} }{\mathrm{6}!}+\frac{\mathrm{x}^{\mathrm{8}} }{\mathrm{8}!}\right)^{\mathrm{2}} \\ $$$$\mathrm{is}\:\frac{\mathrm{2}}{\mathrm{8}!}+\frac{\mathrm{2}}{\mathrm{2}!\mathrm{6}!}+\frac{\mathrm{1}}{\mathrm{4}!\mathrm{4}!}=\frac{\mathrm{1}}{\mathrm{315}} \\…
Question Number 130602 by EDWIN88 last updated on 27/Jan/21 Answered by mr W last updated on 27/Jan/21 $$={number}\:{of}\:\mathrm{4}\:{digit}\:{numbers}\:{which} \\ $$$${are}\:{divisible}\:{by}\:\mathrm{3}: \\ $$$$\mathrm{1002},\:\mathrm{1005},\:…,\:\mathrm{9999} \\ $$$$\Rightarrow\frac{\mathrm{9999}−\mathrm{1002}}{\mathrm{3}}+\mathrm{1}=\mathrm{3000} \\…
Question Number 130193 by mr W last updated on 23/Jan/21 $$\mathrm{How}\:\mathrm{many}\:\mathrm{words}\:\mathrm{with}\:\mathrm{at}\:\mathrm{least}\:\mathrm{2}\:\mathrm{letters} \\ $$$$\mathrm{can}\:\mathrm{be}\:\mathrm{formed}\:\mathrm{from}\:\boldsymbol{\mathrm{UNUSUALNESS}}? \\ $$ Answered by benjo_mathlover last updated on 23/Jan/21 $$\:\mathrm{U}=\mathrm{3},\:\mathrm{N}=\mathrm{2},\:\mathrm{S}=\mathrm{3},\left(\mathrm{A}=\mathrm{L}=\mathrm{E}=\mathrm{1}\right) \\ $$$$\:\mathrm{words}\::\:\mathrm{XX}\:=\:\begin{pmatrix}{\mathrm{3}}\\{\mathrm{1}}\end{pmatrix}\:=\:\mathrm{3}…
Question Number 130034 by EDWIN88 last updated on 22/Jan/21 $$\mathrm{How}\:\mathrm{many}\:\mathrm{integers}\:\mathrm{between}\:\mathrm{999}\:\mathrm{and}\:\mathrm{4000} \\ $$$$\left(\mathrm{both}\:\mathrm{are}\:\mathrm{included}\right)\:\mathrm{can}\:\mathrm{be}\:\mathrm{formed}\:\mathrm{using} \\ $$$$\mathrm{digits}\:\mathrm{0},\mathrm{1},\mathrm{2},\mathrm{3},\mathrm{4}\:\mathrm{if}\:\mathrm{repetition}\:\mathrm{of}\:\mathrm{digits}\:\mathrm{is} \\ $$$$\mathrm{allowed}?\: \\ $$ Answered by liberty last updated on 22/Jan/21…
Question Number 130019 by I want to learn more last updated on 21/Jan/21 $$\mathrm{How}\:\mathrm{many}\:\mathrm{4}\:\mathrm{letters}\:\mathrm{word}\:\mathrm{can}\:\mathrm{be}\:\mathrm{formed}\:\mathrm{from}\:\:\:\:\mathrm{COMMUNICATION} \\ $$ Answered by mr W last updated on 22/Jan/21 $$\mathrm{2}×{C}…
Question Number 63845 by gunawan last updated on 10/Jul/19 $$\underset{{r}=\mathrm{0}} {\overset{{n}} {\sum}}\:^{{n}} {C}_{{r}} \:\frac{\mathrm{1}+{r}\:\mathrm{log}_{{e}} \:\mathrm{10}}{\left(\mathrm{1}+\:\mathrm{log}_{{e}} \:\mathrm{10}^{{n}} \right)^{{r}} }=… \\ $$ Commented by gunawan last updated…
Question Number 63596 by Tawa1 last updated on 05/Jul/19 $$\mathrm{The}\:\mathrm{surnames}\:\mathrm{of}\:\mathrm{40}\:\mathrm{students}\:\mathrm{in}\:\mathrm{a}\:\mathrm{class}\:\mathrm{were}\:\mathrm{arranged}\:\mathrm{in} \\ $$$$\mathrm{alphabetical}\:\mathrm{order}.\:\mathrm{16}\:\mathrm{of}\:\mathrm{the}\:\mathrm{surnames}\:\mathrm{begin}\:\mathrm{with}\:\mathrm{O}\:\mathrm{while} \\ $$$$\mathrm{9}\:\mathrm{of}\:\mathrm{the}\:\mathrm{surnames}\:\mathrm{begin}\:\mathrm{with}\:\mathrm{A}.\:\:\mathrm{14}\:\mathrm{of}\:\mathrm{the}\:\mathrm{letters}\:\mathrm{of}\:\mathrm{the}\: \\ $$$$\mathrm{alphabet}\:\mathrm{do}\:\mathrm{not}\:\mathrm{appear}\:\mathrm{as}\:\mathrm{the}\:\mathrm{first}\:\mathrm{letter}\:\mathrm{of}\:\mathrm{any}\:\mathrm{surname}. \\ $$$$ \\ $$$$\left(\mathrm{i}\right)\:\:\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\mathrm{probability}\:\mathrm{that}\:\mathrm{the}\:\mathrm{surname}\:\mathrm{of}\:\mathrm{a}\:\mathrm{child}\:\mathrm{picked} \\ $$$$\mathrm{at}\:\mathrm{random}\:\mathrm{from}\:\mathrm{the}\:\mathrm{class}\:\mathrm{begins}\:\mathrm{with}\:\mathrm{either}\:\mathrm{A}\:\mathrm{or}\:\mathrm{O} \\ $$$$\left(\mathrm{ii}\right)\:\:\mathrm{If}\:\mathrm{more}\:\mathrm{than}\:\mathrm{one}\:\mathrm{surname}\:\mathrm{begins}\:\mathrm{with}\:\mathrm{a}\:\mathrm{letter}\:\mathrm{besides}\:\mathrm{A} \\…
Question Number 63246 by Tawa1 last updated on 01/Jul/19 $$\mathrm{Arrange}\:\mathrm{these}\:\mathrm{digits}:\:\:\:\:\:\:\mathrm{1}\:\:\mathrm{1}\:\:\mathrm{2}\:\:\mathrm{2}\:\:\mathrm{3}\:\:\mathrm{3}\:\:\mathrm{4}\:\:\mathrm{4} \\ $$$$\:\:\:\:\:\:\mathrm{So}\:\mathrm{that}\:\mathrm{the}\:\mathrm{1}'\mathrm{s}\:\mathrm{are}\:\mathrm{four}\:\mathrm{digit}\:\mathrm{apart} \\ $$$$\:\:\:\:\:\:\mathrm{So}\:\mathrm{that}\:\mathrm{the}\:\mathrm{2}'\mathrm{s}\:\mathrm{are}\:\mathrm{three}\:\mathrm{digit}\:\mathrm{apart} \\ $$$$\:\:\:\:\:\:\mathrm{So}\:\mathrm{that}\:\mathrm{the}\:\mathrm{3}'\mathrm{s}\:\mathrm{are}\:\mathrm{two}\:\mathrm{digit}\:\mathrm{apart} \\ $$$$\:\:\:\:\:\:\mathrm{So}\:\mathrm{that}\:\mathrm{the}\:\mathrm{4}'\mathrm{s}\:\mathrm{are}\:\mathrm{one}\:\mathrm{digit}\:\mathrm{apart} \\ $$$$ \\ $$ Commented by mr…
Question Number 62022 by Tawa1 last updated on 14/Jun/19 Answered by MJS last updated on 14/Jun/19 $$\mathrm{3}. \\ $$$$\mathrm{even}:\:\mathrm{2}×\mathrm{6}=\mathrm{12} \\ $$$$\mathrm{uneven}:\:\mathrm{3}×\mathrm{2}=\mathrm{6} \\ $$$$\mathrm{12}+\mathrm{6}=\mathrm{18} \\ $$$$\mathrm{4}.…
Question Number 62014 by Tawa1 last updated on 14/Jun/19 Answered by MJS last updated on 14/Jun/19 $$\mathrm{1} \\ $$$$\mathrm{5}×\mathrm{6}=\mathrm{30} \\ $$$$\mathrm{2} \\ $$$$\mathrm{4}×\mathrm{3}×\mathrm{2}=\mathrm{24} \\ $$…