Question Number 36784 by Joel579 last updated on 05/Jun/18 $$\mathrm{Prove}\:\mathrm{that} \\ $$$$\underset{{r}=\mathrm{0}} {\overset{{n}} {\sum}}\:{r}\:\begin{pmatrix}{{n}}\\{{r}}\end{pmatrix}^{\mathrm{2}} \:=\:{n}\:\begin{pmatrix}{\mathrm{2}{n}\:−\:\mathrm{1}}\\{\:\:{n}\:−\:\mathrm{1}}\end{pmatrix} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 167765 by ArielVyny last updated on 24/Mar/22 $$ \\ $$show that two permutations are conjugate if their matrices are similar Terms of Service…
Question Number 36398 by NECx last updated on 01/Jun/18 $${Consider}\:{triangle}\:{ABC}.{If}\:\mathrm{206} \\ $$$${lines}\:{are}\:{drawn}\:{from}\:{A}\:{to}\:{BC}\:{how} \\ $$$${many}\:{triangles}\:{are}\:{formed}? \\ $$ Commented by Rasheed.Sindhi last updated on 02/Jun/18 $$\mathrm{207}+\mathrm{206}+…+\mathrm{1}=\frac{\mathrm{207}×\mathrm{208}}{\mathrm{2}}=\mathrm{21528} \\…
Question Number 101880 by mr W last updated on 05/Jul/20 $${Find}\:{the}\:{number}\:{of}\:{six}−{digit}\:{odd} \\ $$$${numbers}\:{without}\:{repeated}\:{digits}. \\ $$ Answered by bemath last updated on 05/Jul/20 $$\mathrm{5}×\mathrm{8}×{C}_{\mathrm{4}} ^{\mathrm{8}} ×\mathrm{4}!…
Question Number 101732 by mr W last updated on 04/Jul/20 $$\mathrm{There}\:\mathrm{are}\:\mathrm{10}\:\mathrm{identical}\:\mathrm{mathematics} \\ $$$$\mathrm{books},\:\mathrm{7}\:\mathrm{identical}\:\mathrm{physics}\:\mathrm{books} \\ $$$$\mathrm{and}\:\mathrm{5}\:\mathrm{identical}\:\mathrm{chemistry}\:\mathrm{books}. \\ $$$$\mathrm{Find}\:\mathrm{the}\:\mathrm{number}\:\mathrm{of}\:\mathrm{ways}\:\mathrm{to}\:\mathrm{compile}\: \\ $$$$\mathrm{the}\:\mathrm{books}\:\mathrm{under}\:\mathrm{the}\:\mathrm{condition}\:\mathrm{that} \\ $$$$\mathrm{same}\:\mathrm{books}\:\mathrm{are}\:\mathrm{not}\:\mathrm{mutually}\:\mathrm{adjacent}. \\ $$ Commented by…
Question Number 101393 by bemath last updated on 02/Jul/20 Answered by 1549442205 last updated on 02/Jul/20 $$\mathrm{Suppose}\:\mathrm{the}\:\mathrm{number}\:\mathrm{of}\:\mathrm{cars}\:\mathrm{manufactured} \\ $$$$\mathrm{in}\:\mathrm{the}\:\mathrm{first}\:\mathrm{yeat}\:\mathrm{be}\:\mathrm{n}\:\mathrm{units}\:.\mathrm{Then}\:\mathrm{in}\:\mathrm{the}\:\mathrm{second}\:\mathrm{year} \\ $$$$\mathrm{is}\:\frac{\mathrm{3n}}{\mathrm{2}}\:\mathrm{and}\:\mathrm{in}\:\mathrm{the}\:\mathrm{third}\:\mathrm{year}\:\mathrm{is}\:\mathrm{2n}\:.\mathrm{Sum}\:\mathrm{of}\:\mathrm{cars} \\ $$$$\mathrm{manufactured}\:\mathrm{in}\:\mathrm{the}\:\mathrm{3\_years}\:\mathrm{period}\:\mathrm{is} \\ $$$$\frac{\mathrm{9}\boldsymbol{\mathrm{n}}}{\mathrm{2}\:}.\boldsymbol{\mathrm{Hence}}\:\boldsymbol{\mathrm{P}}=\frac{\frac{\mathrm{3}\boldsymbol{\mathrm{n}}}{\mathrm{2}}}{\frac{\mathrm{9}\boldsymbol{\mathrm{n}}}{\mathrm{2}}}=\frac{\mathrm{1}}{\mathrm{3}}\Rightarrow\boldsymbol{\mathrm{Choose}}\:\boldsymbol{\mathrm{A}}…
Question Number 166787 by nadovic last updated on 27/Feb/22 $$\mathrm{How}\:\mathrm{many}\:\mathrm{permutations}\:\mathrm{of}\:\mathrm{the} \\ $$$$\mathrm{letters}\:\mathrm{of}\:\mathrm{the}\:\mathrm{word}\:\mathrm{EINSTEIN}\:\mathrm{are} \\ $$$$\mathrm{possible}\:\mathrm{if}\:\mathrm{the}\:\mathrm{EIN}\:\mathrm{groups}\:\mathrm{must}\:\mathrm{not} \\ $$$$\mathrm{be}\:\mathrm{next}\:\mathrm{to}\:\mathrm{eachother}? \\ $$ Commented by mr W last updated on…
Question Number 166770 by mr W last updated on 27/Feb/22 $${In}\:{how}\:{many}\:{ways}\:{can}\:{you}\:{go}\:{up}\:{a}\: \\ $$$${staircase}\:{with}\:\mathrm{20}\:{steps}\:{if}\:{you}\:{take}\: \\ $$$${one},\:{two}\:{or}\:{three}\:{steps}\:{at}\:{a}\:{time}? \\ $$ Commented by MJS_new last updated on 27/Feb/22 $$\mathrm{is}\:\mathrm{it}\:\mathrm{121415}?…
Question Number 35640 by NECx last updated on 21/May/18 $${A}\:{panel}\:{of}\:\mathrm{3}\:{women}\:{and}\:\mathrm{4}\:{men}\:{is} \\ $$$${to}\:{be}\:{formed}\:{from}\:\mathrm{8}\:{women}\:{and} \\ $$$$\mathrm{7}\:{men}.{Find}\:{the}\:{number}\:{of}\:{ways} \\ $$$${which}\:{the}\:{panel}\:{can}\:{be}\:{formed}\:{if} \\ $$$${it}\:{must}\:{contain}\:{at}\:{least}\:\mathrm{2}\:{women}. \\ $$ Answered by tanmay.chaudhury50@gmail.com last updated…
Question Number 35639 by NECx last updated on 21/May/18 $${Three}\:{boys},{two}\:{girls}\:{and}\:{a}\:{puppy} \\ $$$${sit}\:{at}\:{a}\:{round}\:{table}.{In}\:{how}\:{many} \\ $$$${ways}\:{can}\:{they}\:{be}\:{arranged}\:{if}\:{the} \\ $$$${puppy}\:{is}\:{to}\:{be}\:{seated} \\ $$$$\left.{i}\right){between}\:{the}\:{two}\:{girls} \\ $$$$\left.{ii}\right){between}\:{any}\:{two}\:{boys} \\ $$ Commented by NECx…